Experimental Investigation on Flutter Similitude of Thin-Flat Plates

In this article we investigate the influence of a rectangular microchannel aspect ratio on the liquid–liquid flow. An ionic liquid was chosen as one of the working fluids due to a vast scope of applications. Immiscible ionic liquid-water flow in T-shaped microchannels with 160μm hydraulic diameter and aspect ratios equal to 2 and 4 was studied experimentally. Flow pattern maps were drawn and compared for two channels in terms of We*Oh dimensionless number. Parallel flow was shown to prevail for the channel with higher aspect ratio. The influence of channel aspect ratio on plug flow peculiarities was studied in detail. Plug length and velocity were measured at different bulk flow rates. Velocity fields in aqueous plugs were measured using the micro-PTV technique. Velocity circulations were calculated for different flow rates. Total circulation value inside plugs was found to be higher in the channel with the lower aspect ratio.

The validity of scale model impact evaluation of the SST Transportation System is acceptable based on Dimensional Analysis (Buckingham Pi Theorem) and the work of numerous programs that have evaluated the agreement among dimensional analysis, several different reduced-size models and full-scale impact test data. Excellent accuracy has been demonstrated between scale models and full-scale impact data when collected in conformance with the Buckingham Pi Theorem. 20 refs., 4 figs.

Introduction: Side weir structures are extensively used in hydraulic engineering, irrigation and environmental engineering, and it usually consists of a main weir and a lateral channel. Side weirs are also used as an emergency structure. This structure is installed on one side or both sides of the main channel to divert the flow from the main channel to the side channel. Lateral outflow takes place when the water surface in the main channel rises above the weir sill. Flow over a side weir is a typical case of spatially varied flow with decreasing discharge. There have been extensive studies on side weir overflows. Most of the previous theoretical analysis and experimental research works are related to the flow over rectangular side weirs in rectangular main channels. In the current study, the flow conditions over a trapezoidal side weir located in a rectangular main channel in subcritical flow regime is considered. Materials and Methods: The experiments were performed in a rectangular open channel having provisions for a side weir at one side of the channel. The main channel was horizontal with 12 m length, 0.25 m width, and 0.5 m height, and it was installed on a frame; lateral channel that has a length of 6 m, width of 0.25 m, and height of 1 m. It was set up parallel to the main channel; walls and its bed were made up of Plexiglas plates. The side weir was positioned at a distance of 6 m from the channel’s entrance. A total of 121 experiments on trapezoidal side weirs were carried out. Results and Discussion: For trapezoidal side weir, effective non-dimensionnal parameters were identified using dimensional analysis and Buckingham's Pi-Theorem. Finally, the following non-dimensional parameters were considered as the most effective ones on the discharge coefficient of the trapezoidal side weir flow. in which Fr1= upstream Froude number, P= hight of the trapezoidal side weir, y1= upstream water depth, z=side slope of the trapezoidal side weir and T=top flow width of the trapezoidal side weir. Water surface profiles were measured along the weir crest, the main channel centerline, and far from the weir section. Different elevations in water surface profile depend on the upstream Froude number in the main channel; depth differences in low Froude numbers are at minimum values, and in high Froude numbers are at maximum amounts. The water surface level along the crest drops at the entrance of the side weir to the first half of the side weir; and it has been attributed to the side weir entrance effect at the upstream. Afterwards, the water level rises towards the downstream of the weir. According to the experimental results, measurements of the water in the centerline of the main channel are reliable and water surface drop is negligible. According to the parameters affecting the discharge coefficient for each value of z, discharge coefficient equations were developed with acceptable accuracy such that the effects of this parameter were shown separately. Finally, the general equation was proposed. The general functional form for discharge coefficient is presented as follows where the effect of the side slope parameter, z, is also considered. The mean and maximum percentage errors of the discharge coefficient computed using the proposed equation are as 2.6% and 11.5% , respectively. Conclusion: In this study, the characteristics of trapezoidal side weir overflows in subcritical flow regime were discussed. For this purpose, experimental data related to the water surface profile of the side weir and discharge coefficient were collected and analyzed. The results showed that the most efficient section for measuring water surface profile is located at the center line of the main channel. It was found that for trapezoidal side weir, the discharge coefficient depends on the Froude number, the ratio of crest height to initial depth, the overflow length to initial depth, and the side slope of the weir. In this study, conventional trapezoidal weir theory has been used in order to evaluate the discharge coefficient and provide side weir discharge equation. For this purpose, three reference depths were considered for conventional weir, and for each depth an equation was developed for the discharge coefficient. Comparison between predicted values and experimental data showed that average flow depth results in accurate outcomes for assessing the discharge coefficient. The average value of error for discharge coefficient estimation by the proposed equation is 2.6%. Thus this equation is proposed for use in practice by water engineers. Keywords: Control structure, Conventional weir, Discharge coefficient, Spatially varied flow, Trapezoidal side weir, Water surface profile

This paper deals with the investigations on the thermal performance of a vertically oriented closed loop pulsating heat pipe (VCLPHP), both experimentally and by the use of dimensionless numbers. The working fluids used are acetone, ethanol, methanol and heptane. The VCLPHP consists of copper capillary tubes bent into five turns. The tube’s inner and outer diameters are 2 mm and 3 mm, respectively, and are made of copper. The lengths of the evaporator, adiabatic and condenser sections are 50 mm, 90 mm and 70 mm, respectively. A constant fill ratio and a constant heat input of 60% and 80W, respectively, were used for the experimental investigations. The evaporator section was heated by means of a strip heater with a heating capacity of 400W. The condenser was cooled by circulating water. The experimental results showed that acetone is a better performer as compared to other fluids in terms of low thermal resistance and high heat transfer coefficient. Heptane showed the lowest thermal performance among all fluids. Ethanol and methanol showed average performance. The dimensional analysis was carried out using Kutateladze number, Prandtl number, Karman number, Bond number and Jacob number. Ethanol which showed an average performance in experimental investigations displayed the best thermal performance in terms of Prandtl number. With respect to Bond number, Karman number and Jacob number, acetone showed the best thermal performance. Heptane showed average thermal performance for all dimensionless numbers. Since the thermal performance of acetone both experimentally and by dimensional analysis was better than other working fluids, it may be considered as a suitable working fluid for application in PHP.

Predicting the dynamic response of elastic-plastic beams by dimensional analysis

Predicting operational capacity of redox flow battery using a generalized empirical correlation derived from dimensional analysis

A method was devised for estimating aspect ratio, wing ratio, wing area, wing loading, and wing length from study skins of bats. These measures were taken of 136 species representing 15 families. Wing area and loading are positively, and wing length negatively, correlated with size. Aspect and tip ratios are independent of size and of each other. Distinctive combinations of some of these variables characterize groups of bats that presumably have similar flight modes. Speed is positively correlated with aspect ratio and tip index, but regresses significantly only on the former. Long tips coupled with low aspect ratio may characterize hoverers. Long wings and short tips may characterize bats that are capable of remaining airborne at slow speeds. Most bats with low aspect ratios are forest dwellers, whereas species with high aspect ratios are migrants and foragers in open areas.

The spatial variability of subreach denitrification rates in streams was evaluated with respect to controlling environmental conditions, molecular examination of denitrifying bacteria, and dimensional analysis. Denitrification activities ranged from 0 and 800 ng‐N gsed−1 d−1 with large variations observed within short distances (<50 m) along stream reaches. A log‐normal probability distribution described the range in denitrification activities and was used to define low (16% of the probability distribution), medium (68%), and high (16%) denitrification potential groups. Denitrifying bacteria were quantified using a competitive polymerase chain reaction (cPCR) technique that amplified the nirK gene that encodes for nitrite reductase. Results showed a range of nirK quantities from 103 to 107 gene‐copy‐number gsed−1. A nonparametric statistical test showed no significant difference in nirK quantities among stream reaches, but revealed that samples with a high denitrification potential had significantly higher nirK quantities. Denitrification activity was positively correlated with nirK quantities with scatter in the data that can be attributed to varying environmental conditions along stream reaches. Dimensional analysis was used to evaluate denitrification activities according to environmental variables that describe fluid‐flow properties, nitrate and organic material quantities, and dissolved oxygen flux. Buckingham's pi theorem was used to generate dimensionless groupings and field data were used to determine scaling parameters. The resulting expressions between dimensionless NO3− flux and dimensionless groupings of environmental variables showed consistent scaling, which indicates that the subreach variability in denitrification rates can be predicted by the controlling physical, chemical, and microbiological conditions.

Dimensionless groups, the output of a successful dimensional analysis, are usually developed via Buckingham's pi theorem. Because this theorem provides a necessary but not sufficient condition for a solution, such a dimensional analysis may, on occasion, appear to fail. The paper presents the necessary and sufficient conditions in a simple form and builds on them to demonstrate how new physical knowledge can augment a ‘primitive’ set of dimensions to arrive at an optimal number of dimensionless groups. The formulation is used to elucidate the historical Rayleigh-Ria-bouchinsky controversy and a related thermomechanical problem is analysed to demonstrate the complete ‘new knowledge’ algorithm. Mathematica code is appended which incorporates these ideas and generates the complete set of admissible dimensionless groups for any specific problem.

Structures in various industries are exposed to dynamic loads. The dissipative properties of adhesively bonded joints can contribute to the damping of dynamically stressed structures. Dynamic hysteresis tests are carried out to determine the damping properties of adhesively bonded overlap joints by varying the geometry and test boundary conditions. The dimensions of the overlap joints are full-scale and thus relevant for steel construction. Based on the results of experimental investigations, a methodology is developed for the analytic determination of the damping properties of adhesively bonded overlap joints for various specimen geometries and stress boundary conditions. For this purpose, dimensional analysis is carried out using the Buckingham Pi Theorem. In summary, it can be stated that the loss factor of adhesively bonded overlap joints investigated within this study is in the range between 0.16 and 0.41. The damping properties can particularly be increased by increasing the adhesive layer thickness and reducing the overlap length. The functional relationships of all the test results shown can be determined by dimensional analysis. An analytical determination of the loss factor considering all identified influencing factors is enabled by derived regression functions with a high coefficient of determination.

Crystal growth velocity was measured in a mercurous chloride system in a two-zone transparent furnace as a function of the Rayleigh number by varying a/L, where a is the radius of the growth tube and L is the transport length. Growth velocity data showed different trends at low and high aspect ratio, a result that does not support the velocity-aspect ratio trend predicted by theories. The system cannot be scaled on the basis of measurements done at a low aspect ratio. Some change in fluid flow behavior occurs in the growth tube as the aspect ratio increases.

The effect of aspect-ratio (AR) on the formation and interaction of vortical structures in the wake of normal thin flat plates is examined at Re \(=\) 1200 using an infinite span (2D) plate and rectangular plates (\({ AR}=1.0\), 1.6 and 3.2). The vortex shedding frequency significantly increased for \({ AR}=3.2\) compared to the 2D plate, while it dropped for \({ AR}=1.6\) and 1.0. The lowest frequency of vortex shedding was observed for \({ AR}=1.0\). Shear layers rolled to form vortices closer to the plate leeward surface at higher AR. The mean recirculation length was longer for the 2D plate compared to rectangular and square plates. The interaction of shear layers originating at the edges of the rectangular plates led to the formation of vortex loops in the wake. The wake appeared less organized for the lower AR plate (1.6) with a higher turbulence energy compared to \({ AR}=3.2\). The magnitude of turbulence kinetic energy was lowest at \({ AR}=3.2\) and it increased with decreasing AR. The mean drag coefficient was \(\approx \)2 for the 2D plate and \(\approx \)1 for \({ AR}=1\), which suggested major differences in the wake structures.

Adiabatic cooling effectiveness, as a primary indicator of film cooling performance, still suffers from the disputable measurement principle in transonic flow. The two measuring techniques in the state of the art, linear regression method and dual linear regression technique, produce different results, due to their distinct treatment of local recovery temperature. To resolve this controversy, this paper first established a criterion for judging the two methods, based on similarity/dimensional analysis. It is concluded that adiabatic cooling effectiveness is uniquely determined by six dimensionless numbers: Mach number, Reynolds number, Prandtl number of the mainstream, blowing ratio, momentum ratio and temperature ratio between coolant and mainstream. Then, the two methods were gauged against the judging criterion through transient thermal measurements by infrared thermography, for transonic flow over a flat plate with film cooling. All the six dimensionless numbers were fixed during experiments. Only the value of mainstream temperature and coolant temperature varied by 8K and 14K respectively. It is shown that adiabatic cooling effectiveness obtained by linear regression method is roughly unaltered at different mainstream and coolant temperatures, when the coolant-to-mainstream temperature ratio is fixed. However, results measured by dual linear regression technique display noticeable variation (by a maximum of 0.3) under the same circumstance. This is because the assumption of this technique conflicts with the similarity principle. Therefore, linear regression method aligns much better with the judging criterion based on dimensional analysis, than dual linear regression technique, and is hence recommended to measure adiabatic cooling effectiveness in transonic flow.

Non-dimensionalization and three-dimensional flow regime map for fluidization analyses

Dimensional analysis is taught early in an undergraduate curriculum for mechanical engineering, usually during the very first course in fluid mechanics. Such analysis has its roots in the work of Lord Rayleigh, and the mechanics of the process as typically taught to undergraduates follows directly from the classic paper due to Buckingham on what is now known as the Pi Theorem. Students are meant to learn that dimensional analysis is a powerful tool for: developing insight with respect to flow physics, creating new models of physical processes, guiding the performance of experiments and flowfield simulations, aiding the sensible presentation of technical results, and fostering the replication of experiments and simulations. Unfortunately, the usual method for finding non-dimensional products taught to undergraduates requires the selection of scaling variables that can seem arbitrary and the solution of a number of sets of simultaneous equations that is typically tedious and prone to simple errors of arithmetic. As a consequence, students often fail to gain the intended appreciation for the usefulness of dimensional analysis. Fortunately, another technique for forming Π products that does not suffer from these same drawbacks was presented by the late Prof. B. S. Massey of University College London. This paper is intended to disseminate his so-called “step-by-step method” to a wider audience and thus to encourage the adoption of the technique for use in undergraduate curricula.