On Criticality for a Generalized Couette Flow of a Branch-Chain Thermal Reactive Third-Grade Fluid with Reynold’s Viscosity Model

This research considers the third-grade liquid flow and criticality branched-chain of a thermal reaction in a Couette generalized medium with a nonlinear viscosity model. A dimensionless transformation of the system momentum and heat equations are carried out. Compared with the diffusion coefficient, the flow is stimulated by initiation reaction rate, reaction branch-chain order, non-Newtonian term, thermal Grashof number, and pressure gradient. The reactive fluid is fully exothermic with consumption of the material, and the heat exchange in the system is greater than the exchange of heat with the ambient. A semianalytical collocation weighted residual scheme is employed for the branch-chain slice bifurcation, dimensionless energy, and momentum solutions. The results show that exponential decreases in the thermal fluid viscosity can help in controlling the boundless heat produced by the Frank-Kamenetskii term and initiation reaction rate. Therefore, the results will help in stimulating positive combustion processes.

Experimental Investigation of the Size Effect of the Mode I Static Fracture Toughness of Limestone

To study the size effect of the fracture toughness of notched semicircular bend (NSCB) specimens, the dimensionless energy release rate equation of the NSCB specimen was deduced on the basis of the Bažant energy release rate. The influence of the crack length and the specimen size on the fracture toughness was analyzed. The Bažant scale equation was obtained using the International Union of Laboratories and Experts in Construction Materials, Systems, and Structures (RILEM) method. Finally, the Bažant equation was used to analyze the fracture toughness of an NSCB specimen with a radius of 75 mm, and the degree of variation was predicted. The results show that a longer fracture is correlated with a lower fracture toughness value for the same sample size and that a larger specimen radius is correlated with a higher fracture toughness value for the same crack length. The obtained Bažant equation correctly reflects the scale law of the fracture toughness of the NSCB specimen and provides highly accurate predictions of the fracture toughness of large specimens, with an error of not more than 3%. The results obtained in this study provide a new reference method and theoretical basis for the future testing work.

Parameterization of variations for wave energy over bottom slopes

Wave energy transfer through a shallow water region, produced by nonlinearity, was investigated using random wave simulations based on JONSWAP spectra in a physical experiment. To confirm the role of topography, slopes of β = 1/15, 1/30, and 1/45 were installed in a flume. The shoaling effect was first examined by comparing the experimental data with the theoretically predicted values. A wavelet-based bispectrum was then used to investigate the role of the bottom slope in energy transfer. Next, the evolution of energy transfer in the total, primary, and higher harmonic frequency bands was investigated using the wavelet-based energy spectrum. Based on the data from each slope, empirical formulas expressing the dimensionless energy parameters as a function of the local water depth were derived. The bottom slope was confirmed to have an influence on the variation in the total energy and primary harmonic energy, but its effect was shown to be negligible for the higher harmonic energy. Novel formulas were derived to represent the combined slope effect.

A Unified Energy Feature of Vortex Rings for Identifying the Pinch-Off Mechanism

Owing to the limiting effect of energy, vortex rings cannot grow indefinitely and thus pinch off. In this paper, experiments on the vortex rings generated using a piston-cylinder apparatus are conducted so as to investigate the pinch-off mechanisms and identify the limiting effect of energy. Both theoretical and experimental results show that the generated vortex rings share a unified energy feature, regardless of whether they are pinched-off or not. Moreover, the unified energy feature is quantitatively described by a dimensionless energy number γ, defined as γ=(E/I2Γωmax) and exhibiting a critical value γring = 0.14 ± 0.01 for the generated vortex rings. This unified energy feature reflects the limiting effect of energy and specifies the target of vortex ring formation. Furthermore, based on the tendency of γ during vortex ring formation, criteria for determining the two timescales, i.e., pinch-off time and separation time, which correspond to the onset and end of pinch-off process, respectively, are suggested.

Correlations for mixing energy in processes using Rushton turbine mixer‡

This study reports the research results on a mixing process using a stirred tank mixer under the action of a rotating magnetic field (RMF). Dimensionless correlations are proposed to predict the power consumption and mixing time for the mixing systems analysed. The results suggest that the mixing behaviour of the experimental set-ups tested may be assessed using the dimensionless mixing energy as the product of the power input and mixing time. In addition, an innovative strategy is proposed on the basis of the synergistic effect of the rotational Rushton turbine and the RMF generator. The values of the dimensionless energy thus obtained were used to compare the mixing process performed by the mixing devices tested. It is shown that the mixing process under the RMF action has significantly higher values of energy consumption than the conventional Rushton turbine. The total energy consumption for the mixing process performed by the RMF mixer may be reduced by concomitant use of a rotational agitator.

Unsteady flow and heat transfer of Jeffrey fluid over a stretching sheet

The boundary layer flow and heat transfer of an incompressible Jeffrey fluid have been investigated. The analytic solutions of the arising differential system have been computed by homotopy analysis method (HAM). The dimensionless expressions for wall shear stress and surface heat transfer are also derived. Exact solutions of the momentum equation and numerical solutions of the dimensionless energy equations have been obtained for the steady-state case. The results indicate an increase in the velocity and the boundary layer thickness by increasing the elastic parameter (Deborah number) for a Jeffrey fluid.

Investigation on Similar Law of Drag Reduction Performance of Supersonic Vehicle Induced by Laser Energy

Wave drag is high when vehicle flights in supersonic, which impacts on aerodynamic performance of the vehicle heavily, so how to reduce wave drag becomes an important problem which needs to be solved. As an active-controlling technology on flow, drag reduction by laser energy deposition has been paid more and more attention to by researchers. Based on Euler equations, mechanical model and numerical method of drag reduction induced by laser plasma are established. Effect on drag reduction performance of hemispherical blunt body of laser energy, blunt size, temperature and pressure of surrounding gas is studied. A dimensionless energy factor is extracted according to numerical results. Results indicate: drag reduction percentage increases with dimensionless energy factors increasing when dimensionless energy factor is less than 0.7; when dimensionless energy factor is greater than 0.7, energy will reach saturation, and drag reduction percentage keeps constant approximately; power efficiency decreases with dimensionless energy factors increasing. Therefore, similar law of drag reduction performance by laser plasma is obtained preliminarily, which provides possibility for reliable amplification of drag reduction by laser energy deposition.

Invariants for slightly heated decaying grid turbulence

The paper examines the validity of velocity and scalar invariants in slightly heated and approximately isotropic turbulence generated by passive conventional grids. By assuming that the variances $\langle {u}^{2} \rangle $ and $\langle {\theta }^{2} \rangle $ ($u$ and $\theta $ represent the longitudinal velocity and temperature fluctuations) decay along the streamwise direction $x$ according to power laws $\langle {u}^{2} \rangle \sim {(x- {x}_{0} )}^{{n}_{u} } $ and $\langle {\theta }^{2} \rangle \sim {(x- {x}_{0} )}^{{n}_{\theta } } $ (${x}_{0} $ is the virtual origin of the flow) and with the further assumption that the one-point energy and scalar variance budgets are represented closely by a balance between the rates of change of $\langle {u}^{2} \rangle $ and $\langle {\theta }^{2} \rangle $ and the corresponding mean energy dissipation rates, the products $\langle {u}^{2} \rangle { \lambda }_{u}^{- 2{n}_{u} } $ and $\langle {\theta }^{2} \rangle { \lambda }_{\theta }^{- 2{n}_{\theta } } $ must remain constant with respect to $x$. Here ${\lambda }_{u} $ and ${\lambda }_{\theta } $ are the Taylor and Corrsin microscales. This is unambiguously supported by previously available data, as well as new measurements of $u$ and $\theta $ made at small Reynolds numbers downstream of three different biplane grids. Implications for invariants based on measured integral length scales of $u$ and $\theta $ are also tested after confirming that the dimensionless energy and scalar variance dissipation rate parameters are approximately constant with $x$. Since the magnitudes of ${n}_{u} $ and ${n}_{\theta } $ vary from grid to grid and may also depend on the Reynolds number, the Saffman and Corrsin invariants which correspond to a value of $- 1. 2$ for ${n}_{u} $ and ${n}_{\theta } $ are unlikely to apply in general. The effect of the Reynolds number on ${n}_{u} $ is discussed in the context of published data for both passive and active grids.