Modified Diffusion Model of Pseudo-Shock Waves Considering Upstream Boundary Layers

The length of a pseudo-shock was estimated with a new momentum balance model. In this simple model, it is presumed that there is no wall friction in the region of the pseudo-shock. Inflow conditions are specified at a boundary sufficiently upstream of the pseudo-shock. The outflow boundary condition is applied with, for example, specified pressure or choking. The outflow impulse function is balanced with the inflow impulse function, the wall friction upstream of the pseudo-shock, and the reaction force from the wall. The starting position of the pseudo-shock is determined through balance of the forces in this model, and the length of the pseudo-shock is also determined. The model was applied to several kinds of flow fields, for example, straight ducts with and without a backward-facing step, and divergent ducts. The model was also applied to the diffuser of an ejector-jet, in which two gases flowed in parallel. The calculated results reasonably agreed with the experimental results within the scope of preliminary application. The starting position of the pseudo-shock was primarily dominated by the reaction force in the divergent duct. Several features of the pseudo-shock were discussed with the present model. (7) and (17) a = papameter of Eq. (7) B = parameter of Eqs. (7) and (17) 2 JAXA Research and Development Report JAXA-RR-06-037E e = outflow f = friction i = inflow p = pseudo-shock, state at the exit of pseudo-shock r = reaction step = step t = total th = throat w = wall 1 = upstream of pseudo-shock, entrance, primary flow 1b = after bleeding and upstream of pseudoshock 2 = downstream of pseudo-shock, secondary flow

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“…2,[7][8][9] Crocco proposed a shockless model. 2 In his model, the dissipative region spreads toward the isentropic region.…”

Section: Introductionmentioning

confidence: 99%

“…As for the length of the pseudo-shock, many researchers tried to present a way of estimation of the length. Ikui and others have presented modifications 7,8 to the Crocco model and have estimated length of the pseudo-shock. Zimont and Ostras have also presented a modification 9 of the Crocco model.…”

Section: Introductionmentioning

confidence: 99%

Momentum Balance Model of Flow Field with Pseudo-Shock

Kanda

Tani

2005

43rd AIAA Aerospace Sciences Meeting and Exhibit

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“…Ikui et al (1974a) argued that the pseudo-shock should not be regarded as a shock but as "dissipative phenomenon of the high speed flow in the central region with the low speed flow near the wall." From this reasoning, Ikui et al introduce a 'diffusion model' (Ikui et al, 1974a), followed by the 'modified diffusion model' (Ikui et al, 1981), and they found favourable agreement with their experimental data for both models. Both the shock-less model by Crocco (1958) and the diffusion model by Ikui et al (1974a), which is a modified form of the shock-less model, both give the same flow properties Literature Review at the end of the pseudo-shock, which is the same as the flow downstream of a normal shock.…”

Section: Pseudo-shock and Shock Train Analytical Modelsmentioning

confidence: 97%

“…According to Matsuo et al (1999) from a review of previous studies (Ikui et al, 1974a(Ikui et al, , 1981Nussdorfer, 1954;Shapiro, 1953) At low Mach numbers (1.0 < M < 1.2) the transition from supersonic to subsonic flow is via a single normal shock. Where the shock meets the wall there is a shock boundary layer interaction, which is a highly complex fluid phenomenon in its own right.…”

Section: Shock Train and Pseudo-shock Experimentsmentioning

confidence: 99%

“…There are a number of pseudo-normal-shock and shock train models in the literature, with varying degrees of agreement with experimental data; such as the diffusion model (Ikui et al, 1974a), the modified diffusion model (Ikui et al, 1981), the submerged jet model (Zimont and Ostras, 1976), the momentum balanced model (Kanda and Tani, 2005) and the shock reflection model (Tamaki et al, 1971) to name a few. Crocco (1958) was the first to propose a shock train model, which is depicted in Figure 2.12.…”

Section: Pseudo-shock and Shock Train Analytical Modelsmentioning

confidence: 99%

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Investigation of pre-combustion shock trains in a sramjet using a shock tunnel at Mach 8 flight conditions

Ridings¹

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One of the major challenges to scramjet propulsion is the ability to operate over a wide range of Mach numbers. The dual-mode scramjet has the advantage that it can operate much like a ramjet at low Mach numbers, with subsonic flow entering the combustion chamber, and as a conventional scramjet at higher Mach numbers where the flow remains supersonic throughout the engine. A dual-mode scramjet is able to operate as a ramjet by allowing a shock train to form in the section between the inlet and combustor known as the isolator. This pre-combustion shock train, which is a series of intersecting shock and expansion waves, provides additional compression of the flow allowing subsonic flow to be supplied to the combustion chamber.Free-piston shock tunnels, such as Stalker Tubes, are typically used to test scramjet engines due to the high enthalpy flows which these facilities can produce. However these impulse type wind tunnels have short test times of the order of milliseconds. As the pre-combustion shock train involves large regions of separated flow, which take longer than attached flow to establish, there is some question as to whether dual mode can be modelled in Stalker Tubes.This work investigates whether pre-combustion shock trains can be studied in shock tunnels at the upper end of the dual-mode regime and if so, how this phenomenon affects scramjet performance. Experiments were conducted in the T4 Stalker Tube at The University of Queensland at a condition which represents flight at Mach 8 at an altitude of 26 km. This corresponds to a dynamic pressure of 105 kPa and a total enthalpy of 3.1 MJ kg −1 .The experiments were conducted using a simple axi-symmetric scramjet, which comprised a short inlet, an isolator, fuel injectors and three interchangeable combustion chambers. The set of combustion chambers consisted of a constant area and two divergent combustors with half-cone angles of 1 • and 2 • . The different combustion chambers were tested to assess the effect which area expansion has on the shock train and on the overall combustion efficiency of the engine. The model was arranged in a semi-direct connect configuration to produce the desired conditions at the isolator entrance. Gaseous hydrogen was used as the fuel and was injected via six port-hole injectors equally spaced around the circumference. Wall static pressures were measured along the isolator and combustor walls. A quasi-one-dimensional cycle analysis code, ii which is capable of modelling separated flow, is used to model the flow through the engine and provides estimates of the combustion efficiency and distribution of heat release.Robust combustion was observed in the experiments over a range of fuel equivalence ratios between 0.5 and 1.35, for all three combustor configurations. Results for the constant area combustor show that at an equivalence ratio approximately equal to 0.7 the boundary layer separates due to the pressure rise generated from combustion, forming a shock train upstream of fuel injection. With increasing equivalence...

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