Aerodynamic Design of a Laval Nozzle for Real Gas Using Hodograph Method

We propose an approach for the design of the subsonic part of plane and axisymmetric Laval nozzles for real gases. The proposed approach is based on the hodograph method and allows one to solve the inverse design problem directly. Real gas effects are taken into consideration using the chemical equilibrium model. We present nozzle contours computed with the proposed method for a stoichiometric methane-air mixture. Results confirm that real gas effects have a strong influence on the nozzle shape. The described method can be used in the design of nozzles for rocket engines and for high-enthalpy wind tunnels.

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Sensitivity of Supersonic ORC Turbine Injector Designs to Fluctuating Operating Conditions

Volume 2B: Turbomachinery ◽

10.1115/gt2015-42193 ◽

2015 ◽

Cited By ~ 5

Author(s):

Elio A. Bufi ◽

Paola Cinnella ◽

Xavier Merle

Keyword(s):

Method Of Characteristics ◽

Organic Rankine Cycle ◽

Design Procedure ◽

Rankine Cycle ◽

Operating Conditions ◽

Real Gas ◽

Real Gas Effects ◽

Nozzle Shape ◽

Turbine Design ◽

The Impact

The design of an efficient organic rankine cycle (ORC) expander needs to take properly into account strong real gas effects that may occur in given ranges of operating conditions, which can also be highly variable. In this work, we first design ORC turbine geometries by means of a fast 2-D design procedure based on the method of characteristics (MOC) for supersonic nozzles characterized by strong real gas effects. Thanks to a geometric post-processing procedure, the resulting nozzle shape is then adapted to generate an axial ORC blade vane geometry. Subsequently, the impact of uncertain operating conditions on turbine design is investigated by coupling the MOC algorithm with a Probabilistic Collocation Method (PCM) algorithm. Besides, the injector geometry generated at nominal operating conditions is simulated by means of an in-house CFD solver. The code is coupled to the PCM algorithm and a performance sensitivity analysis, in terms of adiabatic efficiency and power output, to variations of the operating conditions is carried out.

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Supercooling in hypersonic nitrogen wind tunnels

Journal of Fluid Mechanics ◽

10.1017/s0022112094001564 ◽

1994 ◽

Vol 269 ◽

pp. 283-299 ◽

Cited By ~ 2

Author(s):

Wayland C. Griffith ◽

William J. Yanta ◽

William C. Ragsdale

Keyword(s):

Vibrational Energy ◽

Ideal Gas ◽

Wind Tunnels ◽

Pure Nitrogen ◽

Real Gas ◽

Absolute Limit ◽

Real Gas Effects ◽

Supercooled Region ◽

The Ideal

Recent experimental observation of supercooling in large hypersonic wind tunnels using pure nitrogen identified a broad range of non-equilibrium metastable vapour states of the flow in the test cell. To investigate this phenomenon a number of real-gas effects are analysed and compared with predictions made using the ideal-gas equation of state and equilibrium thermodynamics. The observed limit on the extent of supercooling is found to be at 60% of the temperature difference from the sublimation line to Gibbs’ absolute limit on phase stability. The mass fraction then condensing is calculated to be 12–14%. Included in the study are virial effects, quantization of rotational and vibrational energy, and the possible role of vibrational relaxation and freezing in supercooling. Results suggest that use of the supercooled region to enlarge the Mach–Reynolds number test envelope may be practical. Data from model tests in supercooled flows support this possibility.

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Experimental Verification of Real Gas Effects in High-Enthalpy Flows

Shock Waves @ Marseille II ◽

10.1007/978-3-642-78832-1_3 ◽

1995 ◽

pp. 15-24

Author(s):

G. Eitelberg

Keyword(s):

Experimental Verification ◽

Real Gas ◽

High Enthalpy ◽

Real Gas Effects

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Experimental Facilities and Measuring Techniques

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100071601 ◽

1959 ◽

Vol 63 (585) ◽

pp. 493-502 ◽

Cited By ~ 4

Author(s):

D. W. Holder

Keyword(s):

High Temperature ◽

Wind Tunnels ◽

Real Gas ◽

Hypersonic Flight ◽

Measuring Techniques ◽

Hypersonic Speeds ◽

Real Gas Effects ◽

Experimental Facilities ◽

Very High ◽

Introductory Review

SummarySome of the aerodynamic problems that arise in flight at hypersonic speeds can be studied experimentally with wind tunnels and measuring techniques that do not differ in principle from those used for research on supersonic flow. If, however, it is required to simulate the very high temperatures of hypersonic flight, it is usually necessary to use heaters and tunnels of unconventional design, frequently having a very short running time, or to make tests with a model launched or propelled at high velocity.The short running times sometimes involve the use of measuring techniques that differ considerably from those of conventional wind tunnel practice. Also, in the presence of high temperature, real gas effects, it is sometimes necessary to measure additional quantities in order to define the state of the gas. The paper contains a brief introductory review of these topics, and of the extent to which experimental test facilities can reproduce the conditions of full-scale hypersonic flight.

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The interaction of a shock wave with a laminar boundary layer at a compression corner in high-enthalpy flows including real gas effects

Journal of Fluid Mechanics ◽

10.1017/s0022112097005673 ◽

1997 ◽

Vol 342 ◽

pp. 1-35 ◽

Cited By ~ 36

Author(s):

S. G. MALLINSON ◽

S. L. GAI ◽

N. R. MUDFORD

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Shock Wave ◽

Gas Flows ◽

Perfect Gas ◽

Experimental Conditions ◽

Real Gas ◽

High Enthalpy ◽

Compression Corner ◽

Real Gas Effects

The high-enthalpy, hypersonic flow over a compression corner has been examined experimentally and theoretically. Surface static pressure and heat transfer distributions, along with some flow visualization data, were obtained in a free-piston shock tunnel operating at enthalpies ranging from 3 MJ kg−1 to 19 MJ kg−1, with the Mach number varying from 7.5 to 9.0 and the Reynolds number based on upstream fetch from 2.7×104 to 2.7×105. The flow was laminar throughout. The experimental data compared well with theories valid for perfect gas flow and with other relevant low-to-moderate enthalpy data, suggesting that for the current experimental conditions, the real gas effects on shock wave/boundary layer interaction are negligible. The flat-plate similarity theory has been extended to include equilibrium real gas effects. While this theory is not applicable to the current experimental conditions, it has been employed here to determine the potential maximum effect of real gas behaviour. For the flat plate, only small differences between perfect gas and equilibrium gas flows are predicted, consistent with experimental observations. For the compression corner, a more rapid rise to the maximum pressure and heat transfer on the ramp face is predicted in the real gas flows, with the pressure lying slightly below, and the heat transfer slightly above, the perfect gas prediction. The increase in peak heat transfer is attributed to the reduction in boundary layer displacement thickness due to real gas effects.

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High-enthalpy flow over a rearward-facing step – a computational study

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.29 ◽

2012 ◽

Vol 695 ◽

pp. 405-438 ◽

Cited By ~ 12

Author(s):

N. R. Deepak ◽

S. L. Gai ◽

A. J. Neely

Keyword(s):

Reynolds Number ◽

Computational Study ◽

Finite Rate ◽

Real Gas ◽

High Enthalpy ◽

Flow Features ◽

The Face ◽

Real Gas Effects ◽

Computational Fluid Dynamics Cfd ◽

Two Temperature

AbstractHypersonic, high-enthalpy flow over a rearward-facing step has been numerically investigated using computational fluid dynamics (CFD). Two conditions relevant to suborbital and superorbital flow with total specific enthalpies of $26$ and $50~\mathrm{MJ} ~{\mathrm{kg} }^{\ensuremath{-} 1} $, are considered. The Mach number and unit Reynolds number per metre were 7.6, 11.0 and $1. 82\ensuremath{\times} 1{0}^{6} $, $6. 23\ensuremath{\times} 1{0}^{5} $ respectively. The Reynolds number based on the step height was correspondingly $3. 64\ensuremath{\times} 1{0}^{3} $ and $12. 5\ensuremath{\times} 1{0}^{2} $. The computations were carried out assuming the flow to be laminar throughout and the real gas effects such as thermal and chemical non-equilibrium are studied using Park’s two-temperature model with finite-rate chemistry and Gupta’s finite-rate chemistry models. In the close vicinity of the step, detailed quantification of flow features is emphasised. In particular, the presence of the Goldstein singularity at the lip and separation on the face of the step have been elucidated. Within the separated region and downstream of reattachment, the influence of real gas effects has been identified and shown to be negligible. The numerical results are compared with the available experimental data of surface heat flux downstream of the step and reasonable agreement is shown up to 30 step heights downstream.

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