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Experimental design of counter-flow vortex tubes with varying diameters for multi-nozzle at high-pressure applications using the Taguchi method

  • Raman Vilhekar and Sukanta Roga ORCID logo EMAIL logo
Published/Copyright: December 29, 2025
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International Journal of Turbo & Jet-Engines
From the journal International Journal of Turbo & Jet-Engines

Abstract

This study investigates the impacts of nozzle number, orifice diameter, vortex tube diameter, cold end temperature, cold mass fraction, and inlet air pressure using experimental analysis and Taguchi methods. In contrast, the current study conducts eight trials to examine the chosen output response. Furthermore, 2ˆ3 trials are needed because there are three impacts of those parameter components and two levels for each factor. Based on the specifications, the L8 (2ˆ3) orthogonal array with two levels each is chosen. The significance levels and control elements for a single- and a double-nozzle are contrasted. To determine the response values for each of the eight run conditions, several experiments are conducted. For a single nozzle, maximum efficiency is found at 7 bar. For trial 2, a cold mass fraction of 0.37 yields an efficiency of 24.74 %. For the double nozzle, the optimal conditions for maximum cooling performance and COP are 8 bar pressure, 0.38 cold mass fraction, and 35 °C cold end temperature. The analysis is used to create graphs, regression equations, and analysis of variance (ANOVA) tables.

Keywords: ANOVA; cold end temperature difference; cooling capacity; COP; Taguchi method
Corresponding author: Sukanta Roga, Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur, 440010, India, E-mail:

Acknowledgement

The author expresses his sincere gratitude to the Visvesvaraya National Institute of Technology, Nagpur.

  1. Research ethics: Not applicable. This study does not involve human participants or animals.

  2. Author contributions: The authors have accepted equal responsibilities for the entire content of this manuscript and approved its submission.

  3. Use of Large Language Models, AI and Machine Learning Tools: No AI or Machine Learning tools were used for data generation, analysis, interpretation, or drawing scientific conclusions. The authors take full responsibility for the content of the manuscript.

  4. Conflict of interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  5. Research funding: This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

  6. Data availability: Not applicable.

  7. Consent for publication: Not applicable. This manuscript does not contain any individual person’s data in any form (including individual details, images, or videos).

Nomenclature

Abbreviation

RHVT

Ranque-Hilsch vortex tube

VT

Vortex tube

FRL

Filter, regulator, lubricator

DOE

Design of experiments

S/N

Signal-to-Noise ratio

OA

Orthogonal array

ANOVA

Analysis of Variance

COP

Coefficient of Performance

L/D

Length-to-diameter ratio

TAE

Thermoacoustic engine

TAR

Thermoacoustic refrigerator

Symbol

L

Length of vortex tube

D

Diameter of vortex tube

L/D

Length-to-diameter ratio

D c

Cold end orifice diameter

D n

Inlet nozzle diameter

N

Number of inlet nozzles

θ

Cone angle of hot valve (°)

P in

Inlet air pressure (bar)

T in

Inlet air temperature (°C)

T c

Temperature at cold end (°C)

T h

Temperature at hot end (°C)

ΔT c

Cold temperature drop = Tin−Tc (°C)

ΔT h

Hot temperature rise = Th−Tin (°C)

m˙ c

Mass flow rate at cold end (kg/s)

m˙ t

Total inlet mass flow rate (kg/s)

μ

Dynamic viscosity (Pa·s)

γ

Specific heat ratio (Cp/Cv)

R

Universal gas constant (J/kg·K)

η

Isentropic Efficiency (%)

Q c

Cooling capacity (W)

ϕ

Cold mass fraction = m˙c/m˙t

ψ h

Dimensionless pressure drop parameter (hot end)

η 1

Optimized efficiency indicator

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Received: 2025-10-04
Accepted: 2025-12-03
Published Online: 2025-12-29

© 2025 Walter de Gruyter GmbH, Berlin/Boston

https://doi.org/10.1515/tjj-2025-0099
Keywords for this article
ANOVA; cold end temperature difference; cooling capacity; COP; Taguchi method
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