Mohammed K. Ibrahima (corresponding author), A. F. Abohelwab and Galal B. Salemc Lecturer, Aerospace Engineering Department, Faculty of Engineering, University of Cairo, Giza, 12613 Egypt E-mail: email@example.com Currently Assistant Professor, Aerospace Engineering Department, Graduate School ofEngineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan E-mail: firstname.lastname@example.org b Industrial Engineering Consultant, 88 Ramsis-2, Nasr City, Cairo, Egypt c Chairman and Professor, Aerospace Engineering Department, School of Engineering, University of Cairo, Giza 12613, Egypt
Abstract The supersonic wind tunnel is an indispensable facility for basic education in anycourse that covers compressible ﬂows and one of the main pillars of any aerodynamic laboratory. The introduction of a supersonic wind tunnel at the aerodynamics laboratory of the Aerospace Engineering Department at Cairo University had often been postponed and was hindered by a lack of funds for the purchase of foreign equipment and expertise. Thoughts therefore turned to building such facilityinstead of buying it, substituting high-tech and complex foreign equipment for locally produced equipment, and ‘thinking out of the box’ to make the most use of available resources, even when this led to some unconventional applications. An extensive scheme for the design, fabrication, and realization of a multi-Mach number (M = 1.5, 2, and 2.5) supersonic wind tunnel for laboratory experiments isproposed in this paper. The proposed scheme is simple, detailed and multi-level; it starts by utilizing one-dimensional isentropic ﬂow theory for the conceptual design phase and makes full use of computational ﬂuid dynamics at the detailed design phase. This ensured that we had a working design before we embarked on the manufacture of any components, which would have been costly to modify had therebeen any design error. A parametric study has been carried out for a number of design parameters, using numerical simulations. After the design and fabrication, a number of successful standard textbook experiments, for Mach number 2, were carried out as validation for the proposed scheme. The results showed good agreement with the theoretical predictions. Keywords compressible ﬂow; wind tunneltesting; supersonic ﬂow; computational ﬂuid dynamics; isentropic ﬂow; method of characteristics; shock waves
Notation m ˙ A a M p R T u, v mass ﬂow rate cross-sectional area speed of sound Mach number pressure gas constant temperature Cartesian perturbed velocity components
International Journal of Mechanical Engineering Education 37/4
Supersonic wind tunnel
V x, y β γ Φ ϕ′ ρ θ ij
ﬂow velocity Cartesian coordinates shock wave angle speciﬁc heat ratio velocity potential function small perturbation potential function density cone semivertex angle unit vector in the x-direction unit vector in the y-direction
Subscripts 1 condition upstream of normal shock wave 2 condition downstream of normal shock wave e nozzle exit condition o stagnation condition Superscripts *critical condition at which M = 1 ` perturbation component normalized by critical speed of sound ∼ full velocity components = a + u or a + v Introduction Supersonic wind tunnels have been used for research, development, and teaching for more than ﬁve decades. Aerodynamics, propulsion, and acoustic testing are some of their main uses. The tunnel consists of a nozzle block, test section, and adiffuser. Details on various aspects of the supersonic wind tunnel and its components can be found in texts by Anderson [1, 2]. The problems encountered in supersonic wind tunnel design and operation include a high pressure ratio at the start of supersonic ﬂow in the test section, insufﬁcient supply of dry air, wall interference effects, and the need to use fast instrumentation for intermittent...