Shear Stress Transfer Model Research Articles

Heat transfer performance of supercritical CO2 in a vertical U-tube

Supercritical carbon dioxide (sCO2) is taken as an excellent working medium for efficient and compact energy conversion devices. However, heat transfer performance (HTP) of sCO2 in a vertical U-tube is intricate owing to dramatic variation of its temperature-dependent thermophysical properties. In this study, flow and heat transfer performance (FHTP) of sCO2 in a vertical U-tube is studied with an improved shear stress transfer model. Additionally, the impacts of operational parameters (heat flux q, mass flux G and pressure P), flow directions and bending diameters (dbend) of U-tube on FHTP are investigated. In both directions, the differences in local pressure drop caused by buoyancy effect and thermal expansion are analyzed deeply. The results demonstrate that the bend section can disturb flow and vortexes persist in downstream, thus improve the HTP. However, an apparent heat transfer deterioration zone can be observed in the ascending section. Under both directions, the average heat transfer coefficient (havg) raises with the growing G and P and decreasing q and dbend, while the total pressure drop (ΔPtotal) rises with the raising G and q as well as decreasing P. Moreover, the U-tube with down-up direction obtains higher havg and lower ΔPtotal than up-down.

Improved SST turbulence model for supersonic flows with APG/separation

A goal in modeling the turbulent flows in computational fluid dynamics is to find an empirical yet universal model to address the complex scenarios. Menter's Shear Stress Transfer (SST) [1] is a Reynolds-Averaged Navier-Stokes (RANS) based two-equation turbulence model and has been one of the most widely used turbulence models for numerical simulation of viscous flows. However, in some practical cases on supersonic, the standard SST model shows unsatisfactory prediction of flow separation and the often underestimation of Reynolds stress. The error mainly comes from the inappropriate use of Bradshaw's assumption which is proposed under turbulent kinetic energy (TKE) equilibrium flow conditions. This paper proposes an improved SST turbulence model which combines the structural parameter with the ratio of the turbulence generation term to the dissipation term and imposes a mixing function to correct the logarithmic and wake parts of the region. Several supersonic test cases are carried out to verify the new model. The calculation results show that the new model exhibits better performance in capturing the separation zones than the baseline model (BSL) and the standard SST model.

Achieving Best Turbine Blade Cooling Efficiency from a Cylindrical Cooling Hole with Reverse-Vortex Generator Using Numerical Simulation

This investigation bargains mathematical investigation of the impact of kidney vortex generation (KVG) on the film cooling execution of a round cooling opening which has measurement (d = 20 mm) on a level plate. The collection between the stream cooling air and standard hot gases will result kidney vortex which will wipe out the film cooling adequacy. Two kind of reverse vortex generator (RVG) with various statures (H = 0.5 d and 0.25 d) are intended to eliminate the kidney vortex and examine best film cooling adequacy, where every one of them is mounted to the level plate upstream of the cooling opening by changing its parallel positions (A = 0.0 d, 0.25 d, 0.5 d and 0.75 d) concerning the opening community line and for each kind has diverse distance regard to opening focus line. The changing of blowing proportion (BP = 0.5-1.0) was considered in this investigation. The simulation model was used to simulate the formation of film cooling using a shear stress transfer (SST) model by Workbench 15 software. The outcomes have been introduced in terms of laterally averaged and maximum value of film cooling comparison diagrams, vorticy on x/d = 3.0 and film cooling distribution which clarified how the outcomes acquired. The Cases 04 and 07 gave the best situations for RVG where case 04 gave wide covered for laterally average film cooling efficiency (η = 0.35), while case 07 gave the highest expansion distribution and the maximum value for film cooling efficiency (η = 0.66). The best results are obtained when the blowing ratio (BP = 0.5) due to a lower velocity of cooling air which will made best interaction with the hot air (main stream)which will represent the hot gases in real case.

Investigation of high strain rate effects on strain-hardening cementitious composites using Voronoi-cell lattice models

Strain-hardening cementitious composites (SHCC) have been reported in several studies to exhibit in several studies to exhibit high toughness even under extreme dynamic loads. To understand such dynamic behavior of SHCC, this study extends a previously developed rate-dependent lattice model by introducing a non-local formulation of the fiber-matrix interface behavior. The Voronoi-cell lattice model, representing the cementitious matrix, employs an explicit time integration scheme and a visco-plastic unit to account for the inertia effect and Stefan effect. Additionally, randomly-distributed short fibers were modeled using an analytical model of shear stress transfer at the fiber-matrix interface. The proposed numerical model successfully simulated the direct tensile behavior and multiple cracking patterns of SHCC, revealing distinct rate-dependent failure characteristics. Through a simple parameter fitting process, the model accurately predicted the dynamic increase factor (DIF) of strength and strain capacity of high-speed tensile experiments. Furthermore, the numerically evaluated rate dependency of the fiber-matrix interface exhibited identical trends to previous experimental studies. Finally, the influences of fluctuations in the applied strain rate during actual high-speed loading tests and the random dispersion of fibers were assessed.

Modeling of the flow and heat exchange in pipes with turbulators of viscous heat carriers in the laminar region, as well as in the transition to turbulent flow

Objective. Mathematical modeling of heat transfer in pipes with turbulators for viscous heat carriers at Reynolds numbers characteristic of laminar and transient flow regimes is carried out by the calculation method. The solution of the heat exchange problem for semicircular cross-section flow turbulators based on multiblock computing technologies based on the solution of the Reynolds equations (closed for the transient mode using the Menter shear stress transfer model) and the energy equation (on multi-scale intersecting structured grids) by the factorized finite-volume method (FCOM) was considered.Method. The calculation was carried out on the basis of a theoretical method based on the solution of the Reynolds equations, closed for transient modes using the Menter shear stress transfer model, and the energy equation on multiscale intersecting structured grids (FCOM), by a factorized finite-volume method.Result. Both local and averaged characteristics of the flow and heat exchange in pipes with turbulators for a viscous coolant for laminar and transient flow modes of the coolant were obtained using the FCOM method in the work, which made it possible to determine for these modes the levels of heat exchange intensification that satisfactorily correlate with the existing experiment.Conclusion. The calculated relative hydraulic resistance for low turbulators increases quite slightly, and for medium-altitude turbulators reaches 2÷2.5 to the critical Reynolds number, and subsequently it increases up to 3 times; for high turbulators, the relative hydraulic resistance increases up to 4 times even before the transition flow regime is reached, after which it increases up to 4.5 times. The calculated relative isothermal intensified heat exchange under the laminar flow regime of a viscous coolant for relatively high turbulators increases almost 2 times; for relatively medium heights of turbulators — almost one and a half, and for low relative heights, the intensification of heat exchange is insignificant.

Mathematical Model of Shear Stress Transfer at Fiber-Matrix Interface of Composite Material

This paper shows a mathematical model of shear stress transfer at the interface between fiber and matrix composite. The stress transfer is a key parameter determining the quality of fiber-matrix interface, which directly correlates with the composite performance as load-bearing structures. The model is derived from the energy balance approach in prior and post fiber cracking. The debonding process is included in the model by implementing traction-separation law. The results show the developed model can predict the shear stress along with the interface. There are significant differences in shear stress by considering the debonding process compared with conventional models. The debonding process must be regarded to assure an accurate evaluation of the interface quality.

Numerical investigation on the transient gas–liquid flow in the rapid switching process of pump turbine

AbstractThe frequent switching of pump mode and turbine mode of the pump turbine leads to frequent transient phenomena. To ensure the safe and stable operation of the unit, a detailed study on the exhaust and pressurization process when the unit switches from turbine mode to the pump mode has been carried out. Based on the Shear Stress Transfer model (SST) k–ω turbulent model, the numerical simulations are processed both in a steady and unsteady state. The visualization results of gas–liquid two phases distribution in the dynamic process of exhaust and pressurization are given, and the characteristic references of each stage are also carried out. The transient characteristics of the torque, axial, and radial force of the runner and guide vane are analyzed by combining the short‐time Fourier transform. The results show that the main frequencies in this transient process are the blade passing frequency and its harmonic frequency. This process also presents a high amplitude band at all frequency values, which may be caused by the entrainment and centrifugal action of the runner on the free liquid surface.

Novel strategies for enhancing hydrodynamic cavitation in a circular Venturi for gas hydrate prevention

The paper considers the problem of hydrate formation, which leads to a significant decrease in the level of production and the creation of a serious threat to the safety of working personnel. A device based on hydrodynamic cavitation to combat hydrate formation is proposed. Based on the turbulence model of shear stress transfer (SST) k-ù, an improved model of non-isothermal fluid flow is presented for the analysis of cavitation processes in the ANSYS CFX program. The model showed that a change in the design features of the cavitator leads to a change in the intensity of its formation, which, in turn, affects the thermodynamic characteristics of the flow. So, with the ratio of the helicoid surface to the length of the neck equal to 0.75, the length of the cavitation cloud was 154 mm, the maximum value of the average gas fraction content was 38%, and the maximum temperature change in the flow flowing through the cavitator reached 1 K. And with the ratio of the above-mentioned geometric parameters equal to 1, the length of the cavitation cloud reaches 245 mm, the maximum value of the average gas fraction content is 60%, and the temperature change of the flow flowing through the cavitator increases to 2 K. A departure from the zone of possible hydrate formation is achieved by increasing the flow temperature. Keywords: Venturi tube; hydrate formation; CFD modeling; cavitation; cavitator.

Mathematical Modelling of Heat Transfer in Pipes with Turbulators in the Laminar Region and in the Transition to Turbulent Flow

The article presents an analysis of mathematical modeling of heat transfer in pipes with turbulators at low Reynolds numbers characteristic of laminar and transient flow modes of heat carriers. The solution of the heat exchange problem for semicircular cross-section flow turbulators based on multi-block computing technologies based on the solution of Reynolds equations closed using the Menter shear stress transfer model and the energy equation (on multi-scale intersecting structured grids) by the factorized finite-volume method is considered. Both local and averaged characteristics of the flow and heat transfer to a pipe with a system of turbulators were obtained, which made it possible to determine the levels of heat exchange intensification for these regime ranges.

Modeling of heat transfer and hydraulic resistance in short and long straight round pipes with semicircular turbulators depending on geometric and operating parameters

Objective. The aim of the study was to determine the dependence of the distributions of average integral hydraulic resistances and convective heat transfer in turbulent flow in pipes with small (short channel) and large (long channel) sequences of semicircular periodic protrusions based on numerical solutions of the Reynolds equation systems, closed using Menter's shear stress transfer models, and energy equations on a multi-scale intersecting structured grid.Method. The calculation technique based on finite volume solutions of the Reynolds equation, closed using the Menter shear stress transfer model and the energy equation on a multi-scale intersecting structured grid, made it possible, with acceptable errors, to calculate the average coefficients of hydraulic resistance and heat transfer in a pipe with different quantities annular semicircular ledges.Result. Analytical comparisons were made of the calculated ratios for relative heat transfer and hydraulic resistance on the number of protrusions in channels with different values of relative heights of turbulators h/D, relative steps between turbulators t/D, different values of the Reynolds criteria Re, with other equivalent parameters, which showed that in in which case the qualitative deviations of the above characteristics are carried out monotonously, and in which case they are accompanied by extrema or inflections, and also showed cases of qualitative changes in the calculated characteristics. With the transition from 30 protrusions to 50, as a rule, only quantitative differences occur for the relative parameters of hydraulic resistance and heat transfer, and their qualitative changes are insignificant; with a further transition from 50 protrusions to 100, their quantitative changes also become insignificant.Conclusion. The nature of the patterns of distributions of the mean integral characteristics of flows and heat transfer for a channel with protrusions of various numbers must be taken into account for a short channel. An analysis of the calculated information obtained showed that when moving from a short channel with turbulators to a long one, most often, there is an increase in relative heat transfer and a decrease in relative hydraulic resistance, which justifies the advantage, from the point of view of intensification, of heat transfer by turbulence of the flow of the last channels in relation to the first channels.

Numerical Simulation of a Periodic Quasi-Switching Mode of Flow around a Conical Dimple with a Slope Angle of 10 Degrees on the Wall of a Narrow Channel Using URANS

The applicability of the solution of the unsteady Reynolds-averaged Navier–Stokes equations (URANS) for the numerical simulation of the periodic quasi-switching regime of vortex generation and heat transfer in a deep conical dimple with a slope angle of 10∘ on the wall of a narrow channel is substantiated. To calculate the turbulent regime, the model of shear stress transfer by Menter 2003, modified taking into account the influence of the curvature of streamlines within the framework of the Rodi-Leshziner-Isaev approach, is used. At Reynolds number Re=104, the oscillation period of the transverse Rz and longitudinal forces Rx, as well as the total heat transfer Numm to the control section of the heated channel wall with a dimple, is set equal to 60, which corresponds to the Strouhal number St=0.0167. Computer visualization of swirling jet-vortex flows demonstrates focus-type sources on the side faces of the dimple. In the self-oscillating mode, a two-cell vortex system is formed with different intensities at the oscillation period Rz. Periodic changes in friction, Nusselt numbers and temperature are recorded in the longitudinal and transverse median sections of the dimple and reflect the oscillations of the vortex structure from left to right and from right to left. The formation of a fan jet is shown, which oscillates relative to the plane of longitudinal symmetry, causing a redistribution of power and thermal loads.

Theory of Heat Transfer in Straight Round Pipes with Square and Triangular Turbulators Under High Reynolds Criteria

Objectives: To carry out mathematical modeling of the structure of vortex zones between periodic flow turbulators with a surface arrangement of triangular and square transverse profiles on the basis of multi-block computing technologies based on solutions of the Reynolds equations (closed by means of the Menter shear stress transfer model) and energy equations (on multi-scale intersecting structured grids) with high Reynolds criteria Re = 106 with an exhaustive analysis of the corresponding current lines. Method: The calculations were carried out on the basis of a theoretical method based on the solution of the Reynolds equations by the factorized finite-volume method, which are closed using the low-Reynolds model of the Menter shear stress transfer, and the energy equation on multi -scale intersecting structured grids (FCOM). Result: Mathematical simulations of the heat exchange process in straight and round pipes with turbulators with d / D = 0.95 ... 0.90 and t / D = 0.25 ... 1.00 square and triangular cross-sections at large Reynolds numbers (Re = 106) on a foundation with multi-block computing technologies, which are based on solutions of the Reynolds equations and energy equations in a finite-volume and factorized way. It is found that the relative intensification of heat transfer [(Nu / Nusm) | Re = 106] / [(Nu / Nusm) | Re = 105] in round pipes with square air turbulators for large Reynolds numbers (Re = 106), which may well be relevant in the channels used in heat exchangers, may be higher with a large-scale increment of hydraulic resistance than for slightly smaller numbers (Re = 105), for relatively high flow turbulators d / D = 0. 90 for the entire range under consideration for the parameter of the relative step between them t / D = 0.25 ... 1.00 a little more than 3%; for turbulators of triangular cross-section, similar indicators are approximately the same. For lower square turbulators with d / D = 0.95, this increase in relative heat transfer for large Reynolds numbers (Re = 106) compared to smaller numbers (Re = 105) does not exceed 6%; for triangular cross-section turbulators, similar indicators are slightly more than 4%. Conclusion: According to the results of calculations based on the developed model, it is possible to optimize the intensification of double turbulators, as well as to control the process of heat transfer intensification. It is shown that for higher square turbulators and at higher Reynolds numbers, a slight increase in the relative Nusselt number Nu / Nusm is accompanied by a significant increase in the relative hydraulic resistance due to the very significant influence of return currents, which can flow directly on the turbulator itself to the greater extent, the higher the Reynolds number; for triangular turbulators, the above trend persists and even deepens.

Theory of Heat Exchange in Pipes With Turbulators With d/D = 0.95 ÷ 0.90 And t/D = 0.25 ÷ 1.00, and Also in Rough Pipes, by Air With Great Reynold’s Numbers Re = 106

Mathematical modeling of heat exchange in air in pipes with turbulators with d / D = 0.95 ÷ 0.90 and t / D = 0.25 ÷ 1.00, as well as in rough pipes, with large Reynolds numbers (Re = 106). The solution of the heat exchange problem for semicircular cross-section flow turbulizers based on multi-block computing technologies based on the factorized Reynolds equations (closed using the Menter shear stress transfer model) and the energy equation (on multi-scale intersecting structured grids) was considered. This method was previously successfully applied and verified by experiment in [1-4] for lower Reynolds numbers. The article continues the computational studies initiated in [1-4,25-27].

Simulation and Experimental Analysis of the Temperature Field of Jet Flow of Aircraft Based on CFD Theory

As a key indicator of airport concrete pavement, the durability of concrete is seriously affected by the jet flow generated by aircraft engines. In order to clarify the temperature field distribution of aircraft jet flow acting on the pavement surface, this paper obtained the temperature field distribution of pavement surface under the action of three types of aircraft jet flow by combining field test experiment and CFD simulation. CFD simulation adopts the shear stress transfer model which is often used in engineering problem calculation, and the field test experiment adopts the method of embedding temperature sensor in precast concrete slab. The paired two sample t test was used to test the difference between the experimental results and the simulation results. The experimental results show that the pavement temperature increases first and then decreases with the distance from the engine, and reaches the maximum at the intersection point of the jet flow and the airport pavement. The simulation curve is in good agreement with the experimental results. When the level of confidence is 0.01, there is no significant difference between the simulation value and the experimental value, which verifies the accuracy and feasibility of the simulation calculation model. The simulation results of the three aircraft showed that when type C aircraft is in the state of full afterforce, the maximum pavement temperature is the highest which is 22m away from the nozzle, and can reach 533.81K. The current work provides a new method for measuring the temperature distribution of airfield pavement under the action of jet flow and a basis for the application of fiber concrete in airfield pavement.

Моделирование процессов аэрогазодинамики элементов конструкции сверхзвукового летательного аппарата

The purpose of the research was to study the aerodynamic features of the flow around the simplest structural elements of an aircraft, such as sharp and blunt-nose cones. For calculations we applied the perfect gas model. To describe flows with large adverse pressure gradients, we used the Menter's shear stress transfer model. We analyzed changes in the aerodynamic characteristics of the cones in a wide range of angles of attack α and flow Mach M∞ numbers. Furthermore, we investigated the parameters of the base region of the sharp cone at transonic and supersonic speeds, and compared the simulation results with the data of a physical experiment both in wind tunnels and on a ballistic installation. The comparison showed good agreement with the experimental data. Numerical simulation data can be applied to form the external appearance of aircraft for various purposes, to study the influence of the temperature factor on the flow around bodies, and to create semi-empirical models for calculating the parameters of the base region of conical bodies.

MODELING OF HEAT EXCHANGE AT TURBULENT FLOW IN FLAT CHANNELS WITH SYMMETRIC TURBULIZERS ON BOTH PARTIES

Objectives. Mathematical modeling of heat transfer in flat channels with turbulators symmetrically located on both its sides, depending on the cross section of the turbulators.Methods. The calculation was carried out on the basis of a theoretical method based on solving the Reynolds equations factorized by the finite-volume finite-volume method, closed using the Menter shear stress transfer model, and the energy equation on multi-scale intersecting structured grids (FCOM), which was successfully tested in [23].Results. The article results of calculating the intensified heat exchange in flat channels with double turbulators of different cross sections (square, rectangular, semicircular, triangular) depending on the determining parameters were quite satisfactorily consistent with the existing experimental material, but having an indisputable advantage over the latter, since the assumptions made in their derivation cover a much wider range of defining parameters than the limitations found in the experiments (Pr=0.7÷100, Re=103÷106, h/dE =0.005÷0.2, t/h=1÷200).Conclusion. According to the results of calculations on the basis of the developed model, it is possible to optimize heat transfer intensification in flat channels with double turbulators of different cross sections, as well as control the heat transfer intensification process. As shown by the calculated data, with the intensification of heat transfer in the flat channels, symmetrical protrusions of square, rectangular and triangular cross sections, i.e. relatively sharp outlines, in the vortices up to the protrusions and behind them the production of turbulence is comparable to energy dissipation, which leads to increased hydraulic losses; for flat channels with protrusions of a semicircular cross section, i.e. relatively smooth outlines, the energy dissipation is much smaller, therefore, the hydraulic resistance in such channels is less. A detailed analysis of the structure of the vortex zones (main, angular, secondary, etc.) between periodic surface flow turbulators of square, semicircular, triangular and rectangular cross sections depending on the geometric and regime parameters of the coolant flow was carried out, the effect of the above vortex zones heat transfer and hydraulic resistance of the channel; additionally confirmed the optimality of application to abrutized turbulators, where hydraulic losses are much smaller than for sharp turbulators, which is directly or indirectly verified by existing experimental material [1—6].

Shear stress transfer model for evaluating the fracture behaviour of SHCCs for RC shear strengthening

This paper presents a numerical shear stress transfer model for investigating the shear fracture behaviour of strain-hardening cementitious composites (SHCCs) for strengthening reinforced concrete (RC) structures. The model focuses on the transferred shear stress on the crack surface of the SHCC, taking account of the contributions from both the contact stress of the matrix and the bridging stress of the fibres. The numerical results demonstrate that the proposed shear stress transfer model can appropriately evaluate the shear fracture behaviour of SHCCs for RC strengthening, in which the fibre bridging effect on the crack surface of the SHCC has much influence on the shear fracture behaviour of the SHCC strengthening layer.

Evaluation of strain-hardening cementitious composites for RC seismic strengthening

A numerical approach for evaluating the behaviour of strain-hardening cementitious composites (SHCCs) for reinforced-concrete (RC) seismic strengthening is presented. The method takes account of the seismic tensile strain capacity of SHCCs for RC strengthening, which is affected by the presence of cracks within the RC and varying layer thickness of the SHCC, the shear transfer behaviour of SHCC layers on the crack surface, which is contributed to by both the contact effect and the fibre bridging effect on the crack surface, and the seismic compressive constitutive law of SHCCs. In the numerical approach, a zero-span tensile model is adopted for reflecting the tensile strain capacity of SHCCs for RC strengthening, and a shear stress transfer model is applied for reflecting the respective contributions of both contact stress and fibre bridging stress for shear stress transfer behaviour of the SHCC on the crack surface. The effectiveness of the numerical approach is confirmed through the comparison between the experimental investigation and numerical analysis, in which the numerical result is coincided with the experimental one.

Estimation of the lifetime of a trapped vortex in a circular cavern on a semicircular airfoil streamlined at a zero angle of attack after switching off slot suction

The restructuring of the periodic structure of a turbulent streamline for a semicircular airfoil at a zero angle of attack with a system of slot suction from the circular cavern switched off is calculated. Multiblock numerical methods are applied for solution of Reynolds-averaged nonstationary Navier–Stokes equations closed using the modified shear-stress transfer model taking into account flow line curvature. The lifetime of a trapped vortex in a circular cavern is estimated.

Numerical approach for evaluating shear failure behavior of strain hardening cementitious composite member

This paper presents a numerical approach for evaluating the shear failure behavior of strain hardening cementitious composite (SHCC) member. The developed approach can clarify the respective contributions of both contact stress and fiber bridging stress for the shear stress transfer behavior on crack surface of SHCC member, which thus can disclose the contribution of fibers to local shear of SHCC member. In the numerical approach, a shear stress transfer model and shear lattice system are proposed, in which the shear lattice system can appropriately express the shape of crack surface, and the shear stress transfer model can accurately quantify the transferred shear stress on the crack surface of SHCC member, focusing on the contribution from both matrix’s contact effect and fiber bridging effect respectively. The effectiveness of the numerical approach is confirmed through the comparison between the experimental and numerical results.