Variation in flow direction requires extensive consideration in the practical application of riblet surfaces. However, studies scarcely examine the impact of flow angle α for riblet, which is usually adopted to reduce flow drag. Accordingly, this research conducted large eddy simulation for a wide range of flow angles. We explored the effect of 0° to 90° flow angle on the surface drag change of Triangular riblet. The time-averaged statistical data and instantaneous flow details indicated that skin friction is decreased with the increase in α . However, pressure drag increased much faster than the friction decrease. Result revealed that skin friction reduction by 4. 537% is obtained when α =0° , and it inhibits turbulence in the spanwise direction. When α ≈ 20° , the total drag reduction disappeared. Within this range, the deviation angle showed little influence on the total drag reduction. When α =90° , skin friction is reduced by 73. 3%; however the pressure drag and total drag increased, accompanied by an increased turbulence. The flow must be nearly parallel to the riblet to achieve drag reduction. Otherwise, the transverse riblet is an effective method to increase the drag.

Various riblet shapes are simulated through the computational fluid dynamics method for the elucidation of riblet effects on turbulent boundary layers and skin friction reduction. For the different shapes, seven typical riblet models are investigated by using renormalization group k-epsilon turbulence models. Simulation results are consistent with the existing theoretical data regarding flat plate and experimental results obtained from the riblet shapes. The riblet velocity profiles cannot satisfy the existing von Ká rmá n’ s constants in the logarithmic law boundary layer. The slope and intercept of the logarithmic law are strongly affected by geometric parameters and riblet shapes, and the effect of geometric parameters can be modeled. Meanwhile, the effects of riblet shapes can be modeled with a shape factor composed of a nondimensional cavity ratio and nondimensional top flatness. Therefore, a uniform model of the boundary layer can be obtained to illustrate the effects of various riblet shapes.

The main goal of this research is to study the drag reduction capabilities of blade-shape riblet surfaces in external flows. For this purpose, the ability of riblet surfaces for drag reduction of an underwater hydrodynamic model has been investigated. The surface geometry has been modified by applying shark skin inspired blade-shape riblets on the surface. These riblets have been modeled in various dimensions and applied on the exterior surface of an underwater hydrodynamic model, and their effects on the exerted drag force, at different flow velocities, have been studied numerically. For validating the numerical solution, the simulation results have been compared with the experimental data obtained by testing an underwater hydrodynamic model in a towing tank laboratory; and the validity of the numerical solution results has been confirmed. The results indicated that, riblet spacing has a significant effect on the reduction of drag force. Furthermore, by increasing the riblet spacing, the drag force is increased rather than decreased. Also, as the velocity increases, the performance of riblets in reducing the drag force is enhanced. In order to minimize the drag force applied on the underwater hydrodynamic model, by analyzing the numerical results, the most optimum riblet spacing has been obtained; at which the drag force is reduced by 7%. The achieved distance is a limit value; and at distances smaller or larger than this optimal distance, the effectiveness of the blade-shape riblet surface in reducing the drag force diminishes.

A Triangular tile latching system consists of a set $\Sigma$ of equilateral Triangular tiles with at least one latchable side and an attachment rule which permits two tiles to get latched along a latchable side. In this paper we determine the language generated by a Triangular tile latching system in terms of planar graphs.

A watching system in a graph G=(V, E) is a set W={w1, w2, …,wk}, where wi=(vi, Zi); viÎ V and Zi is a subset of closed neighborhood of vi such that the sets LW(v) ={wi: vÎZi} are non-empty and distinct, for any v ÎV. In this paper, we study the watching systems of line graph Kn which is called Triangular graph and denoted by T (n). The minimum size of a watching system of G is denoted by w (G). We show that w (T(n))= [2n/3].

In this paper, the hydraulic characteristics of a sharp crested Triangular side weir have been experimentally studied. It was found that the DeMarchi coefficient of discharge for a sharp crested Triangular side weir in subcritical flow is related to the main channel Froude number, the apex angle of weir and ratio of weir height to upstream depth of flow. Suitable equations for discharge coefficient are also obtained.

Interpretation of MR imaging of the wrist may be difficult because of the small size of this joint, its complex anatomy, and its sometimes poorly understood pathologic lesions. A recent study revealed that MR imaging of the wrist influences clinicians' diagnoses and management plans in most patients. Which structures make up the Triangular fibrocartilage complex (TFCC) are not universally agreed upon. In most descriptions, however, the TFCC is composed of the Triangular fibrocartilage (TFC), the meniscus homolog, the ulnar collateral ligament, the dorsal and volar radioulnar ligaments and the sheath of the extensor carpi ulnaris tendon. The ulnolunate and ulnotriquetral ligaments may also be considered as part of the TFCC. These structures are a complex unit that function as a stabilizing element in the pivot movement of the radius and ulna and limit the lateral deviation of the carpus. The distal radioulnar joint is primarily stabilized by the TFCC. The TFC functions as a cushion between the ulnar head and carpal bones. Many of the structures that make up the complex are connected by fibrous bands. This presentation summarizes the current diagnostic criteria that can be useful in interpreting abnormalities of the Triangular fibrocartilage complex (TFCC) of the wrist in this difficult topic in joint MR imaging.