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Influence of ideal nozzle geometry on supersonic flow using the method of characteristics

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Abstract

The present study addresses the application of the method of characteristics (MoC) for determining the thermodynamic and flow properties of the supersonic flow field in the divergent section of an ideal contour nozzle (ICN). An algorithm for developing the wall profile of the ICN using MATLAB programmable finite difference computational functions is discussed. Sixteen ICNs having different geometries are analyzed to study the influence of throat geometric parameters on the properties of the fluid in their divergent section. A sudden change in the Mach number or weak shocks is observed in asymmetric nozzles, i.e., nozzles where the radius of curvature on the convergent and divergent sides is different. Furthermore, it is observed that ICNs with an equal convergent and divergent radius of curvature are capable of developing stable supersonic flow in its divergent section.

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Abbreviations

MoC :

Method of characteristics

ICN :

Ideal contour nozzle

MATLAB :

Matrix laboratories

LRC :

Left running characteristic

RRC :

Right running characteristic

IPS :

Internal point solver

SPS :

Symmetry point solver

IIPS :

Inverse interior point solver

IVL :

Initial value line

M iso :

Iso-Mach

TIC :

Truncated ideal contour

γ :

Ratio of specific heats

R a :

Normalised throat radius of curvature

ρ d, ρ u :

Downstream and upstream radius of curvature

θ in :

Entrance angle

u, v :

Axial and radial velocity components

x, y :

Axial and radial coordinates

δ :

0, 1 for a planar flow and axis-symmetric flow, respectively

V :

Velocity vector in the flow field

a :

Acoustic speed of sound

M :

Mach number

t h :

Throat height

w :

Flow velocity (scalar)

θ :

Angle between flow direction and nozzle axis

ϕ :

Angle between the characteristic line and nozzle axis

R :

Specific gas constant

s :

Length of a characteristic line

ṁ :

Mass flow rate

ζ :

Coefficient of linear axial velocity perturbation

Δθ c :

Angular increment of the downstream circular arc

ṁ num :

Numeric mass flow rate

(ṁ (1−D) ) :

One-dimensional mass flow rate

n :

Number of points taken on IVL

M d :

Desired exit Mach number

α :

Angle between streamline tangent and tangent to characteristic lines

h :

Number of nodes taken on the last LRC

β :

Angle between the nozzle axis and the final LRC

g :

Thermodynamic and flow properties of the fluid as a function of the location

P 0, P :

Stagnation and static pressure

T o, T :

Stagnation and static temperature

ρ o, ρ :

Stagnation and static density

C d :

Discharge coefficient

X s :

First node of IVL on the axis of symmetry

X end :

Last node of IVL extension on the axis of symmetry

L nozzle :

Length of the nozzle

θ exp :

Downstream circular arc expansion angle

A ratio :

Area ratio

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Authors and Affiliations

  1. Department of Mechanical Engineering, Institute of Technology, University of Kashmir, Zakura Campus, Srinagar, 190006, India

    Khalid Rafiq, Mumin Rasheed, Mir Moin Afzal & Junaid H. Masoodi

Authors
  1. Khalid Rafiq
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  2. Mumin Rasheed
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  3. Mir Moin Afzal
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  4. Junaid H. Masoodi
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Corresponding author

Correspondence to Junaid H. Masoodi.

Additional information

Khalid Rafiq is an Engineer at Tata Advanced Systems Limited. He received his B.Tech. in Mechanical Engineering from the Institute of Technology, University of Kashmir. His research interests are computational mechanics and data-driven techniques.

Mumin Rasheed received his B.Tech. in Mechanical Engineering from the Institute of Technology, University of Kashmir. His research interests are engineering fluid mechanics, CFD, aero-thermodynamics, and compressible fluid flow.

Mir Moin Afzal received his B.Tech. in Mechanical Engineering from the Institute of Technology, University of Kashmir. His research interests are AI, robotics, compressible fluid flow, CFD, and aerodynamics.

Junaid H Masoodi is an Assistant Professor of Mechanical Engineering, Institute of Technology, University of Kashmir. He received his Ph.D. in Mechanical Engineering from the National Institute of Technology, Srinagar. His research interests include CFD analysis of turbomachinery, compressible fluid flow, erosive wear, fracture & fatigue.

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Rafiq, K., Rasheed, M., Afzal, M.M. et al. Influence of ideal nozzle geometry on supersonic flow using the method of characteristics. J Mech Sci Technol 36, 6027–6039 (2022). https://doi.org/10.1007/s12206-022-1118-2

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  • DOI: https://doi.org/10.1007/s12206-022-1118-2

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