Thermal Performance of V-Shaped and X-Shaped Ribs in Trapezoidal Cooling Channels

Convective heat transfer enhancement using rib turbulators is effective for turbine blade internal cooling. Detailed heat transfer measurement of X-shaped ribs in a trapezoidal cooling channel was experimentally conducted using infrared thermography. The novel X-shaped ribs were designed by combining two V-shaped ribs, and more secondary flows generated by the X rib delivered higher heat transfer enhancement. The Reynolds numbers in this study were 10,000, 20,000, and 30,000. These ribs were installed on two opposite walls of a trapezoidal channel in a staggered arrangement. The rib pitch-to-height ratios were 10 and 20, and the rib height-to-hydraulic diameter ratio was 0.128. Results indicated that higher heat transfer distribution was observed in the vicinity of the shorter base in the trapezoidal channel. The full X-shaped ribs and the V-shaped ribs demonstrated the highest Nusselt number ratios among all the cases. Although full X-shaped ribs contributed to higher heat transfer improvement due to intensified secondary flows, they also caused significant pressure loss. Therefore, the cutback X-shaped ribs were proposed by removing a segment in the rib at either upstream or downstream region. Consequently, the upstream cutback X-shaped rib and the V-shaped rib produced the highest thermal performance in this trapezoidal channel.

Silting thickness analysis of regular desilting in rectangular and trapezoidal channel

Silting in river is a dynamic process, so it needs to regular desilting. At present, underwater siltation monitoring is still in its early days and based on experience. This paper puts forward the criterion of discrimination, in which the flood discharge section is decreased by 20%. It used the method of steady uniform flow in open rectangular and trapezoidal channel for calculation. The results show that reference values of dredging thickness in different section forms were determined. Siltation thicknesses of rectangular channel are linearly related to water depth. And the reduction rate of trapezoidal channel has a quadratic function relation with silting thicknesses. They were proportional to channel width and their rates trended to mitigation when the bottom width and flood depth were constant. In addition, the reference value of dredging thickness should be determined by combining with the bottom width, surface width, water depth and other actual situation.

CÓDIGO LIVRE PARA SOLUÇÃO NUMÉRICA DAS EQUAÇÕES DE SAINT-VENANT EM CANAIS TRAPEZOIDAIS ASSIMÉTRICOS

<p>Ondas de cheia em canais e ondas produzidas por manobras em comportas são alguns fenômenos simulados com as equações de Saint-Venant em aplicações de engenharia. Um novo código foi desenvolvido para a solução dessas equações aplicadas a um canal trapezoidal assimétrico, empregando o método de volumes finitos de Lax e Friedrichs. Foi adotada uma linguagem de programação reconhecida por um <em>software</em> livre. Três testes numéricos foram realizados. O primeiro, correspondente à passagem de uma onda de cheia em um canal retangular, apresentou aderência aos resultados obtidos com a solução calculada através do método implícito de Preissmann, com desvio relativo máximo de 1,4% para a velocidade e de 0,81% para a altura de escoamento. O segundo teste resolveu o escoamento em um canal de fundo variado que induz à formação de um ressalto hidráulico. As comparações dos presentes resultados com aqueles de simulações publicadas recentemente resultaram em um desvio máximo de 2,3% para as alturas de escoamento, a montante e a jusante do ressalto hidráulico. Para as posições médias do ressalto hidráulico, o desvio foi de 2,4%. Na terceira comparação, simulou-se um ressalto hidráulico em um canal trapezoidal assimétrico de forte declividade, tendo sido encontrada uma solução com desvios relativos menores que 1% para os escoamentos a montante e a jusante do ressalto, quando comparados aos resultados calculados com o método de MacCormack. A posição média do ressalto nesta terceira comparação apresentou um desvio de 5,5% em relação aos resultados anteriores. Os desvios calculados indicam que o código desenvolvido é capaz de resolver escoamentos variáveis em canais com e sem a formação de ressaltos hidráulicos. Este é um resultado de cunho prático, pois mostra que códigos livres podem ser usados na prática da hidráulica em geometrias não-convencionais.</p><p> </p><p align="center">OPEN SOURCE FOR NUMERICAL SOLUTION OF SAINT-VENAN EQUATIONS IN ASYMMETRIC TRAPEZOIDAL OPEN-CHANNELS</p><p>Flood waves in channels, positive waves produced when operating floodgates, and the hydraulic jump are some phenomena simulated with the Saint-Venant equations in practical engineering applications. A new code was developed to solve these equations applied to an asymmetric trapezoidal channel using the Lax-Friedrichs finite volumes method. A programming language recognized by a free software was used. Three numerical tests were performed. The first, corresponding to the passage of a flood wave in a rectangular channel, showed adherence to results of the solution calculated using the Preissmann implicit method, presenting a maximum relative deviation of 1.4% for the speed and 0.81% for the flow height. The second test solved the flow in a channel with a variable bed that induces the formation of a hydraulic jump. Comparisons of the present results with those of recently published simulations produced a maximum deviation of 2.3% for the flow heights, upstream and downstream of the hydraulic jump. For the mean positions of the hydraulic jump the deviation was 2.4%. In the third comparison a hydraulic jump was simulated in an asymmetric trapezoidal channel with a strong slope, obtaining a solution with relative deviations less than 1% for flows upstream downstream of the jump, when compared to the results calculated with the MacCormack method. The average position of the jump in this third comparison showed a deviation of 5.5% in relation to the former results. The calculated deviations indicate that the developed code is capable of solving variable flows in channels with and without the formation of hydraulic jumps. This is a practical result, because it shows that open codes can be used in the practice of hydraulics in nonconventional geometries.</p>