Symmetries and Related Physical Balances for Discontinuous Flow Phenomena within the Framework of Lagrange Formalism

By rigorous analysis, it is proven that from discontinuous Lagrangians, which are invariant with respect to the Galilean group, Rankine–Hugoniot conditions for propagating discontinuities can be derived via a straight forward procedure that can be considered an extension of Noether’s theorem. The use of this general procedure is demonstrated in particular for a Lagrangian for viscous flow, reproducing the well known Rankine–Hugoniot conditions for shock waves.

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The Present Challenge of Transonic Compressor Blade Design

Volume 2A: Turbomachinery ◽

10.1115/gt2018-75528 ◽

2018 ◽

Cited By ~ 2

Author(s):

A. Hergt ◽

J. Klinner ◽

J. Wellner ◽

C. Willert ◽

S. Grund ◽

...

Keyword(s):

Boundary Layer ◽

Shock Wave ◽

Shock Waves ◽

Unsteady Flow ◽

Flow Behavior ◽

Flow Behaviour ◽

Compressor Cascade ◽

Transonic Compressor ◽

Flow Phenomena ◽

Transonic Cascade

The flow through a transonic compressor cascade shows a very complex structure due to the occuring shock waves. In addition, the interaction of these shock waves with the blade boundary layer inherently leads to a very unsteady flow behaviour. The aim of the current investigation is to quantify this behaviour and its influence on the cascade performance as well as to describe the occuring transonic flow phenomena in detail. Therefore, an extensive experimental investigation of the flow in a transonic compressor cascade has been conducted within the transonic cascade wind tunnel of DLR at Cologne. In this process, the flow phenomena were thoroughly examined for an inflow Mach number of 1.21. The experiments investigate both, the laminar as well as the turbulent shock wave boundary layer interaction within the blade passage and the resulting unsteady behaviour. The experiments show a fluctuation range of the passage shock wave of about 10 percent chord for both cases, which is directly linked with a change of the inflow angle and of the operating point of the cascade. Thereafter, RANS simulations have been performed aiming at the verification of the reproducibility of the experimentally examined flow behavior. Here it is observed that the dominant flow effects are not reproduced by a steady numerical simulation. Therefore, a further unsteady simulation has been carried out in order to capture the unsteady flow behaviour. The results from this simulation show that the fluctuation of the passage shock wave can be reproduced but not in the correct magnitude. This leads to a remaining weak point within the design process of transonic compressor blades, because the working range will be overpredicted. The resulting conclusion of the study is that the use of scale resolving methods such as LES or the application of DNS is necessary to correctly predict unsteadiness of the transonic cascade flow and its impact on the cascade performance.

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Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽

10.3390/fluids4030175 ◽

2019 ◽

Vol 4 (3) ◽

pp. 175 ◽

Cited By ~ 2

Author(s):

Dmitry Bratsun ◽

Vladimir Vyatkin

Keyword(s):

Viscous Flow ◽

Closed Form ◽

General Procedure ◽

Fluid Velocity ◽

Fluid Motion ◽

Boussinesq Approximation ◽

Navier Stokes ◽

Chemical Transformations ◽

Navier Stokes Equation ◽

Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

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Application of Viscous Flow Computations for the Aerodynamic Performance of a Backswept Impeller at Various Operating Conditions

Journal of Turbomachinery ◽

10.1115/1.3262196 ◽

1988 ◽

Vol 110 (3) ◽

pp. 303-311 ◽

Cited By ~ 18

Author(s):

C. Hah ◽

A. C. Bryans ◽

Z. Moussa ◽

M. E. Tomsho

Keyword(s):

Experimental Data ◽

Viscous Flow ◽

Three Dimensional ◽

Aerodynamic Performance ◽

Operating Conditions ◽

Centrifugal Impeller ◽

Flow Phenomena ◽

Overall Performance ◽

Real Flow ◽

Operating Points

Three-dimensional flowfields in a centrifugal impeller with backswept discharge at various operating points have been numerically investigated with a three-dimensional viscous flow code. Numerical results and experimental data were compared for the detailed flowfields and overall performance of the impeller at three operating conditions (optimum efficiency, choke, and near-surge conditions). The comparisons indicate that for engineering applications the numerical solution accurately predicts various complex real flow phenomena. The overall aerodynamic performance of the impeller is also well predicted at design and off-design conditions.

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Discontinuous Flow Phenomena in Gelatine Gels

Nature ◽

10.1038/164584a0 ◽

1949 ◽

Vol 164 (4170) ◽

pp. 584-585 ◽

Cited By ~ 2

Author(s):

V. R. GRAY

Keyword(s):

Discontinuous Flow ◽

Flow Phenomena

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Recent Advances in Simulating Unsteady Flow Phenomena Brought About by Passage of Shock Waves in a Linear Turbine Cascade

Journal of Turbomachinery ◽

10.1115/1.2929303 ◽

1993 ◽

Vol 115 (4) ◽

pp. 687-698 ◽

Cited By ~ 3

Author(s):

J. C. Collie ◽

H. L. Moses ◽

J. A. Schetz ◽

B. A. Gregory

Keyword(s):

Shock Waves ◽

Mechanical Performance ◽

Pressure Ratio ◽

High Pressure Ratio ◽

Large Fluctuations ◽

Blade Row ◽

Flow Phenomena ◽

Response Pressure ◽

Unsteady Effects ◽

Transonic Cascade

High-pressure-ratio turbines have flows dominated by shock structures that pass downstream into the next blade row in an unsteady fashion. Recent numerical results have indicated that these unsteady shocks may significantly affect the aerodynamic and mechanical performance of turbine blading. High cost and limited accessibility of turbine rotating equipment severely restrict the quantitative evaluation of the unsteady flowfield in that environment. Recently published results of the Virginia Tech transonic cascade facility indicate high integrity in simulation of the steady-state flow phenomena. The facility has recently been modified to study the unsteady effects of passing shock waves. Shock waves are generated by a shotgun blast upstream of the blade row. Shadowgraph photos and high-response pressure data are compared to previously published experimental and numerically predicted results. Plots are included that indicate large fluctuations in estimated blade lift and cascade loss.

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Investigation of viscous flow phenomena in a rotating system

PAMM ◽

10.1002/pamm.200910212 ◽

2009 ◽

Vol 9 (1) ◽

pp. 479-480

Author(s):

Andre Zucht ◽

Gert Böhme ◽

Andre Müller

Keyword(s):

Viscous Flow ◽

Rotating System ◽

Flow Phenomena

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Recent Advances in Simulating Unsteady Flow Phenomena Brought About by Passage of Shock Waves in a Linear Turbine Cascade

Volume 1: Turbomachinery ◽

10.1115/92-gt-004 ◽

1992 ◽

Cited By ~ 1

Author(s):

J. C. Collie ◽

H. L. Moses ◽

J. A. Schetz ◽

B. A. Gregory

Keyword(s):

Shock Waves ◽

Mechanical Performance ◽

Pressure Ratio ◽

High Pressure Ratio ◽

Large Fluctuations ◽

Blade Row ◽

Flow Phenomena ◽

Response Pressure ◽

Unsteady Effects ◽

Transonic Cascade

High-pressure ratio turbines have flows dominated by shock structures that pass downstream into the next blade row in an unsteady fashion. Recent numerical results have indicated that these unsteady shocks may significantly affect the aerodynamic and mechanical performance of turbine blading. High cost and limited accessibility of turbine rotating equipment severely restrict the quantitative evaluation of the unsteady flowfield in that environment. Recently published results of the Virginia Tech transonic cascade facility indicate high integrity in simulation of the steady state flow phenomena. The facility has recently been modified to study the unsteady effects of passing shock waves. Shock waves are genarated by a shotgun blast upstream of the blade row. Shadowgraph photos and high-response pressure data are compared to previously published experimental and numerically predicted results. Plots are included which indicate large fluctuations in estimated blade lift and cascade loss.

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Shock Waves and Disturbed Flow Phenomena in Arrester with a Gap for Distribution Systems

IEEJ Transactions on Power and Energy ◽

10.1541/ieejpes1990.118.4_406 ◽

1998 ◽

Vol 118 (4) ◽

pp. 406-412

Author(s):

Maki Sakae ◽

Masahisa Otsubo ◽

Chikahisa Honda ◽

Hiroshi Nieda

Keyword(s):

Shock Waves ◽

Distribution Systems ◽

Disturbed Flow ◽

Flow Phenomena

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The Present Challenge of Transonic Compressor Blade Design

Journal of Turbomachinery ◽

10.1115/1.4043329 ◽

2019 ◽

Vol 141 (9) ◽

Cited By ~ 2

Author(s):

Alexander Hergt ◽

J. Klinner ◽

J. Wellner ◽

C. Willert ◽

S. Grund ◽

...

Keyword(s):

Boundary Layer ◽

Shock Wave ◽

Shock Waves ◽

Unsteady Flow ◽

Flow Behavior ◽

Complex Structure ◽

Compressor Cascade ◽

Transonic Compressor ◽

Flow Phenomena ◽

Transonic Cascade

The flow through a transonic compressor cascade shows a very complex structure due to the occurring shock waves. In addition, the interaction of these shock waves with the blade boundary layer inherently leads to a very unsteady flow behavior. The aim of the current investigation is to quantify this behavior and its influence on the cascade performance as well as to describe the occurring transonic flow phenomena in detail. Therefore, an extensive experimental investigation of the flow in a transonic compressor cascade has been conducted within the transonic cascade wind tunnel of DLR Institute of Propulsion Technology at Cologne. In this process, the flow phenomena were thoroughly examined for an inflow Mach number of 1.21. The experiments investigate both the laminar and the turbulent shock wave boundary layer interaction within the blade passage and the resulting unsteady behavior. The experiments show a fluctuation range of the passage shock wave of about 10% chord for both cases, which is directly linked with a change of the inflow angle and of the operating point of the cascade. Thereafter, Reynolds-averaged Navier–Stokes (RANS) simulations have been performed aiming at the verification of the reproducibility of the experimentally examined flow behavior. Here, it is observed that the dominant flow effects are not reproduced by a steady numerical simulation. Therefore, a further unsteady simulation has been carried out to capture the unsteady flow behavior. The results from this simulation show that the fluctuation of the passage shock wave can be reproduced but not in the correct magnitude. This leads to a remaining weak point within the design process of transonic compressor blades because the working range will be overpredicted. The resulting conclusion of this study is that the use of scale-resolving methods such as LES or the application of DNS is necessary to correctly predict unsteadiness of the transonic cascade flow and its impact on the cascade performance.

Download Full-text