Flow and Heat Transfer in a High-Aspect-Ratio Rib-Roughed Cooling Channel with Longitudinal Intersecting Ribs

This paper describes a detailed numerical investigation of a stationary high-aspect-ratio rib-roughed rectangular cooling channel with longitudinal intersecting ribs near the gas turbine blade trailing edge region. In order to overcome the heat transfer performance degeneration in the highaspect- ratio channel, longitudinal intersecting ribs are arranged on the channel bottom surface. The effect of the number of longitudinal intersecting ribs on the flow and heat transfer is systematically studied in the Reynolds number range Re = 10 000–30 000. The results show that a heat transfer augmentation region exists just downstream the junction between the longitudinal rib and the angled rib due to additional secondary flows. With more longitudinal intersecting ribs, the heat transfer distributions on the channel surfaces are more uniform. Though the pressure loss is also enlarged with an increase in the number of longitudinal intersecting ribs, the overall thermal efficiency increases in the entire range of Reynolds numbers investigated. The configuration with two sets of longitudinal intersecting ribs shows the best overall thermal efficiency.     

Stress–Strain Analysis of Smooth and Ribbed Shells under Local Loads

Static problems for smooth and discretely reinforced cylindrical shells under local loads and complex boundary conditions are solved. The stress–strain states of the casing and ribs are determined by the technical theory of shells and the Kirchhoff–Clebsch theory of rods, respectively. The reinforcing elements are arranged eccentrically. They are of equal or different stiffness, which is also variable along the length. The problems are solved using the finite-difference method. Theoretical results obtained from a refined mesh are compared with experimental data     

Stability of open circular cylindrical shells reinforced with longitudinal ribs

We obtain exact and approximate solutions to buckling problems for circular cylindrical open shells hinged at all edges and quasiregularly reinforced with discrete longitudinal ribs. It is shown that analogous solutions to natural-vibration problems for such shells can easily be found Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 83–92, December 2008.     

Heat transfer distribution in rectangular ducts with V-shaped ribs

 Heat transfer distributions are presented for a rectangular duct with two opposite wide walls arranged with V-shaped ribs pointing upstream or downstream relative to the main flow direction. The rectangular duct has an aspect ratio of 1/8. The parallel V-shaped circular ribs are arranged staggered on the two wide walls. The rib height-to-hydraulic diameter ratio is 0.06, with an attack angle of 60°. The pitch-to-height ratio equals 10. The tested Reynolds numbers range from 1000 to 6000. The test surface is sprayed with black paint and then liquid crystal, and a steady state method is adopted to obtain the temperature distribution between adjacent ribs. The secondary flow caused by the angled ribs creates different spanwise variation of the heat transfer coefficient on the rib-roughened wall for different V-rib orientations. Interaction between heat transfer and secondary flow is analyzed. In the streamwise direction, the temperature distribution shows a sawtooth behavior between a pair of adjacent ribs. Local Nusselt numbers are presented between a pair of adjacent ribs, and based on these the average Nusselt numbers are calculated to investigate the augmentation of heat transfer by the presence of the V-shaped ribs. Received on 15 May 2000     

Influence of discrete ribs on the vibrations of rectangular plates

A rectangular plate reinforced with longitudinal ribs is considered. The influence of the discrete ribs on the wavenumbers of harmonic waves propagating along the ribs is investigated. The effect of the stiffness parameters of the ribs on the natural frequencies and modes of a cross-ribbed plate is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 65–78, February 2006.     

Influence of discretely arranged longitudinal ribs on the stability and vibrations of open circular cylindrical shells

Open cylindrical shells reinforced with quasiregular sets of longitudinal ribs and hinged at all edges are considered. The effect of the discrete arrangement and number of ribs on the critical stresses that cause instability under longitudinal compression and on the minimum natural frequencies of vibrations is examined. Numerical results are analyzed     

Propagation of harmonic waves in longitudinally reinforced cylindrical shells with low shear stiffness

The exact solutions of the equations of motion derived under refined theories of shells and ribs based on the Timoshenko model are used to plot dispersion curves for harmonic waves propagating along a cylindrical shell reinforced with discrete longitudinal ribs __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 37–41, May 2006.     

求解水下纵向加肋无限长非圆柱壳声辐射问题的一种新的半解析方法

基于齐次扩容精细积分法和复数矢径虚拟边界谱方法，利用Fourier积分变换和稳相法，提出了一种具有较高效率和精度的新的求解水下纵向加肋无限长非圆柱壳声辐射问题的半解析方法．考虑了非圆柱壳和肋骨之间同时存在多种相互作用力和力偶矩，较已往很多学者仅计及法向相互作用力更加符合实际．不仅比较了该文方法和精确解计算纵向加肋圆柱壳在集中点力激励下的声辐射计算结果，同时还研究了肋骨数量、大小以及椭圆柱壳横截面椭圆度对声辐射特性的影响．数值计算结果表明该文方法较已有的混合FE-BE法更为有效．     

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation effectiveness and precision, is presented for solving the acoustic radiation from a submerged infinite non-circular cylindrical shell stiffened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work,besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The effects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efficient than the existing mixed FE-BE method.     

大型纵向加筋截断锥壳稳定性的半离散分析

如何计算大型纵向加筋截断锥壳的稳定问题，尚未见到有关报导。本文在沿纵向和环向分别采用Ｈｅｒｍｉｔｅ插值和三角级数插值的基础上，建立了几何非线性带筋环单元，进而导出了半离散分析法，并经过实例检验了它的正确与可靠。这样，本文为建立各类工程结构的半离散单元提出了一种新的途径。     

Effect of the stiffness of ribs on the vibrations and stability of open cylindrical shells

The effect of the stiffness of ribs on the minimum natural frequencies and critical stresses of axially compressed open cylindrical shells reinforced with a quasiregular set of longitudinal ribs is analyzed by way of numerical examples. It is shown that the earlier discovered phenomenon of abrupt decrease in the minimum frequencies is independent of rib stiffness for certain modes and a small number of ribs     

Propagation of harmonic waves along open circular cylindrical shells reinforced with a quasiregular set of discrete longitudinal ribs

We obtain the exact solution describing the propagation of harmonic waves along an open cylindrical shell reinforced with a quasiregular set of discrete longitudinal ribs. Numerical examples are used to examine the effect of discrete ribs on the number and shape of dispersion curves and the effect of the stiffness and inertial characteristics of the ribs on the excitation frequency for given wave parameters     

Influence of Discrete Longitudinal Ribs on Harmonic Waves in Cylindrical Shells

The influence of discrete longitudinal ribs on harmonic waves in cylindrical shells is studied by numerical examples. It is shown that the presence of discrete ribs is manifested as an increased number and changed shape of the dispersion curves     

Experimental investigations on frictional resistance and velocity distribution of rough wall with regularly distributed triangular ribs

The relationship between the flow resistance of a turbulent flow over triangular ribs regularly distributed on a wall surface and the velocity distribution around the ribs was investigated experimentally. A concentric cylinder device composed of an inner test cylinder and an outer cylinder was employed to measure the flow resistance using the torque of the shaft of the inner cylinder and the velocity distribution of the flow around a rib by laser Doppler velocimetry (LDV) simultaneously. We prepared four inner test cylinders having 4, 8, 12 and 16 triangular ribs on the surface with the same interval between them. Each rib had an isosceles right triangle V-shape and a height of 2 mm. To investigate the relationship between flow resistance and velocity distribution, we estimated the frictional drag and pressure drag acting on the surface of the ribs separately using the velocity distribution. Therefore, we could also estimate the total flow resistance using the velocity distribution. As a result of the experiment, the flow resistance and the attachment point downstream of the rib were shown to depend on the distance between ribs. Moreover, the flow resistance estimated using the velocity distribution had good agreement with the flow resistance measured using the torque of the inner cylinder.     

Heat transfer and pressure drop measurements in rib-roughened rectangular ducts

In the present study, the thermal and hydraulic performance of three rib-roughened rectangular ducts is investigated. The aspect ratio of the ducts was 1 to 8, and the ribs were arranged staggered on the two wide walls. Three rib configurations were tested: parallel ribs and V-shaped ribs pointing upstream or downstream of the main flow direction. For all cases, the rib height-to-hydraulic diameter ratio was 0.06, with an attack angle of 60° and a pitch-to-height ratio of 10. The Reynolds number range was from 1000 to 6000. Liquid crystal thermography was employed in the heat transfer experiment to demonstrate detailed temperature distribution between a pair of ribs on the ribbed surfaces. The secondary flows caused by the inclined ribs create a significant spanwise variation of the heat transfer coefficients on the rib-roughened wall with high heat transfer coefficient at one end of the rib and low value at the other. In the streamwise direction between two consecutive ribs, the temperature distribution shows a sawtooth fashion because of flow reattachment. Based on the local heat transfer coefficients, the average Nusselt numbers were estimated as weighted mean values. Isothermal pressure drop data were taken and presented as Fanning friction factors. The ducts are compared to each other by considering both heat transfer and friction factor performance.     

Nonlinear Deformation and Stability of a Noncircular Cylindrical Shell Under Combined Loading with Bending and Twisting Moments

A previously developed technique is used to solve problems of strength and stability of discretely reinforced noncircular cylindrical shells made of a composite material with allowance for the moments and nonlinearity of their subcritical stress–strain state. Stability of a reinforced bay of the aircraft fuselage made of a composite material under combined loading with bending and twisting moments is studied. The effects of straining nonlinearity, stiffness of longitudinal ribs, and shell thickness on the critical loads that induce shell buckling are analyzed.     

非局部杆纵向振动的特性研究

基于非局部理论，研究弹性杆在任意边界约束条件下的纵向振动特性．根据Chebyshev 谱级数建立非局部弹性杆的纵向位移形式．在杆的两端引入纵向约束弹簧，通过设置弹簧刚度系数，模拟经典边界及弹性边界．建立非局部杆的能量表达式，由瑞利-里兹法得到齐次线性方程组，求解对应的矩阵特征值与特征向量问题获得非局部杆的固有频率和振型．通过数值仿真计算，研究非局部特征系数与边界约束条件对非局部杆振动频率的影响．结果表明本文方法合理简便，具有良好的精度，且适用于任意弹性边界条件．     

Effect of the Number of Ribs on a Transient in a Cylindrical Shell under a Disturbing Load*

International Applied Mechanics - A technique to study the transient process of the forced vibrations of a cylindrical shell stiffened with longitudinal ribs is developed. The shell is under an...     

Experimental investigation of convective heat transfer enhancement from 3D-shape heat sources by EHD actuator in duct flow

Heat transfer enhancement from cylindrical heat sources as electronic components established at the bottom of duct with in-line arrangement and also from the bottom by electrohydrodynamic (EHD) actuator has been investigated experimentally. Air flow is drawn to the duct with various Reynolds numbers based on hydraulic diameter of inlet of the test section (Re = 0, 500, 1100, 2500 and 3870) that include natural convection (confined and unconfined cases) and forced convection (laminar and turbulent flows). Wire electrodes are arranged in transverse direction and perpendicular to the main flow with two various arrangements and high voltages are applied up to 30 kV in the wires. The results revealed that the second electrode arrangement (three wires over the ribs) is more effective due to more enhancement of heat transfer and less corona power consumption in comparison with the first one (four wires between the ribs). Also the electric field is obviously more effective for low Reynolds numbers.     

On the deformation of a ribbed cylindrical shell with initial deflection under dynamic loading

The finite-difference method with explicit time coordinate is used to study the dynamic stress-strain state of a cylindrical shell with ribs and initial deflections. A specific numerical example is considered to trace the time evolution of longitudinal and transverse displacements for different parameters of the initial deflection __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 61–66, December 2005.