Asymptotics of streamwise Reynolds stress in wall turbulence

The scaling of different features of streamwise normal stress profiles $\langle uu\rangle ^+(y^+)$ in turbulent wall-bounded flows is the subject of a long-running debate. Particular points of contention are the scaling of the ‘inner’ and ‘outer’ peaks of $\langle uu\rangle ^+$ at $y^+\approxeq ~15$ and $y^+ ={O}(10^3)$ , respectively, their infinite Reynolds number limit, and the rate of logarithmic decay in the outer part of the flow. Inspired by the thought-provoking paper of Chen & Sreenivasan (J. Fluid Mech., vol. 908, 2021, p. R3), two terms of an inner asymptotic expansion of $\langle uu\rangle ^+$ in the small parameter $Re_{\tau }^{-1/4}$ are constructed from a set of direct numerical simulations (DNS) of channel flow. This inner expansion is for the first time matched through an overlap layer to an outer expansion, which not only fits the same set of channel DNS within 1.5 % of the peak stress, but also provides a good match of laboratory data in pipes and the near-wall part of boundary layers, up to the highest $Re_{\tau }$ values of $10^5$ . The salient features of the new composite expansion are first, an inner $\langle uu\rangle ^+$ peak, which saturates at 11.3 and decreases as $Re_{\tau }^{-1/4}$ . This inner peak is followed by a short ‘wall log law’ with a slope that becomes positive for $Re_{\tau }$ beyond ${O}(10^4)$ , leading up to an outer peak, followed by the logarithmic overlap layer with a negative slope going continuously to zero for $Re_{\tau }\to \infty$ .

Measuring the Evolution of Urban Resilience Based on the Exposure–Connectedness–Potential (ECP) Approach: A Case Study of Shenyang City, China

Resilience is a new path to express and enhance urban sustainability. Cities suffer from natural shocks and human-made disturbances due to rapid urbanization and global climate change. The construction of an urban resilient developmental environment is restricted by these factors. Strengthening the comprehensive evaluation of resilience is conducive to identifying high-risk areas in cities, guiding regional risk prevention, and providing a scientific basis for differentiated strategies for urban resilience governance. For this study, taking Shenyang city as a case study, the resilience index system was constructed as an ECP (“exposure”, “connectedness”, and “potential”) framework, and the adaptive cycle model was introduced into the resilience assessment framework. This model not only comprehensively considers the relationship between exposure and potential but also helps to focus on the temporal and spatial dynamics of urban resilience. The results show that the exposed indicators have experienced three spatial evolution stages, including single-center circle expansion, multicenter clustering, and multicenter expansion. The potential index increased radially from the downtown area to the outer suburbs, and the low-value area presented a multicenter pattern. The spatial agglomeration of connectivity indicators gradually weakened. The results reflect the fact that the resilience level of the downtown area has been improved and the resilience of the outer expansion area has declined due to urban construction. The multicenter cluster pattern is conducive to the balance of resilience levels. In terms of the adaptive cycle phases of urban resilience, the first ring has gone through three phases: exploitation (r), conservation (K), and release (Ω). The second and third rings have gradually shifted from the exploitation (r) phase to the conservation (K) phase. The fourth ring has entered the exploitation (r) phase from the reorganization (ɑ) phase. The fifth ring and its surrounding areas are in the reorganization (ɑ) phase. The results provide specific spatial guidance for implementing resilient urban planning and realizing sustainable urban development.

The Effectiveness of Non-Loosening Fasteners

Many people know that bolted fasteners are loosened and they sometimes suffer from the loosening. It is also the case for any plants who have hundreds of thousands of bolts. Any of these bolts may cause serious problems when they are loosened. Many countermeasures are proposed to prevent bolt loosening, but few of them are really effective. So far, only three bolting systems passed NAS 3350 tests. They are Eccentric nuts, based on nut eccentricity, Lock’n bolt, based on outer expansion of bolt threads, and L/R nut, whose principle is not open. As L/R nut is unknown how it works, this paper addresses the effectiveness of the Eccentric nuts and Lock’n bolts and compare them in simulation. The author have been working in bolt system loosening for a long time and succeeded the simulation of the phenomenon. This paper is the continuous work of this research.

Large-Reynolds-number asymptotics of the streamwise normal stress in zero-pressure-gradient turbulent boundary layers

A more poetic long title could be ‘A voyage from the shifting grounds of existing data on zero-pressure-gradient (abbreviated ZPG) turbulent boundary layers (abbreviated TBLs) to infinite Reynolds number’. Aided by the requirement of consistency with the Reynolds-averaged momentum equation, the ‘shifting grounds’ are sufficiently consolidated to allow some firm conclusions on the asymptotic expansion of the streamwise normal stress $\langle uu\rangle ^{+}$, where the $^{+}$ indicates normalization with the friction velocity $u_{{\it\tau}}$ squared. A detailed analysis of direct numerical simulation data very close to the wall reveals that its inner near-wall asymptotic expansion must be of the form $f_{0}(y^{+})-f_{1}(y^{+})/U_{\infty }^{+}+\mathit{O}(U_{\infty }^{+})^{-2}$, where $U_{\infty }^{+}=U_{\infty }/u_{{\it\tau}}$, $y^{+}=yu_{{\it\tau}}/{\it\nu}$ and $f_{0}$, $f_{1}$ are $\mathit{O}(1)$ functions fitted to data in this paper. This means, in particular, that the inner peak of $\langle uu\rangle ^{+}$ does not increase indefinitely as the logarithm of the Reynolds number but reaches a finite limit. The outer expansion of $\langle uu\rangle ^{+}$, on the other hand, is constructed by fitting a large number of data from various sources. This exercise, aided by estimates of turbulence production and dissipation, reveals that the overlap region between inner and outer expansions of $\langle uu\rangle ^{+}$ is its plateau or second maximum, extending to $y_{\mathit{break}}^{+}=\mathit{O}(U_{\infty }^{+})$, where the outer logarithmic decrease towards the boundary layer edge starts. The common part of the two expansions of $\langle uu\rangle ^{+}$, i.e. the height of the plateau or second maximum, is of the form $\,A_{\infty }-B_{\infty }/U_{\infty }^{+}+\cdots \,$with $A_{\infty }$ and $B_{\infty }$ constant. As a consequence, the logarithmic slope of the outer $\langle uu\rangle ^{+}$ cannot be independent of the Reynolds number as suggested by ‘attached eddy’ models but must slowly decrease as $(1/U_{\infty }^{+})$. A speculative explanation is proposed for the puzzling finding that the overlap region of $\langle uu\rangle ^{+}$ is centred near the lower edge of the mean velocity overlap, itself centred at $y^{+}=\mathit{O}(\mathit{Re}_{{\it\delta}_{\ast }}^{1/2})$ with $\mathit{Re}_{{\it\delta}_{\ast }}$ the Reynolds number based on free stream velocity and displacement thickness. Finally, similarities and differences between $\langle uu\rangle ^{+}$ in ZPG TBLs and in pipe flow are briefly discussed.

Axial Swirler Design Influences on NOx Emissions for Premixed Combustion in Gas Turbine Combustors With all the Combustor Air Flow Passing Through the Swirler

This work investigates a single axial swirler combustor using flat bladed axial swirlers at atmospheric pressure, 600K preheat, with premixed propane and air. The aim was to investigate the axial swirler design influences on flame stability and NOx emissions, for fully premixed combustion in a single swirler cylindrical combustor configuration. A reference Mach number of 0.05 at 600K was used, which represents all the combustion air passing through the swirler. This maximum swirler airflow is required for the highest turbine entry temperatures with low NOx emissions. The axial swirler design had only a small influence on the weak extinction, but it had a greater influence on NOx. The swirlers with a large central hub had greater NOx emissions, as this created a larger central recirculation zone and greater residence time of the hottest part of the flame. It was preferable to stabilise the flame with an outer expansion shear layer as this minimised the size of the inner recirculation zone and this minimised the NOx. The influence of the swirl angle, 30, 45 or 60° for the same flow capacity was that the swirler had to be a larger diameter as the vane angle was increased, to keep the blockage and pressure loss the same. This removed the possibility of having either an inner or outer flow expansion for the 60° swirler, but the flow expansions were maximised for the 30° swirler. The effect of the swirl vane angle on NOx was mainly due to the associated changes in the flow expansion. 45° swirlers with no central hub and a large outer expansion were the best design for the lowest NOx emissions and could achieve 15ppm NOx at 15% oxygen at 2000K.

Green’s Function for a Closed, Infinite, Circular Cylindrical Elastic Shell

An acceptable variant of the Koiter–Morley equations for an elastically isotropic circular cylindrical shell is replaced by a constant coefficient fourth-order partial differential equation for a complex-valued displacement-stress function. An approximate formal solution for the associated “free-space” Green’s function (i.e., the Green’s function for a closed, infinite shell) is derived using an inner and outer expansion. The point wise error in this solution is shown rigorously to be of relative order (h∕a)(1+h∕a∣x∣), where h is the constant thickness of the shell, a is the radius of the mid surface, and ax is distance along a generator of the mid surface.