Net-exergetic, hydraulic and thermal optimization of coaxial heat exchangers using fixed flow conditions instead of fixed flow rates

Previous studies optimized the dimensions of coaxial heat exchangers using constant mass flow rates as a boundary condition. They show a thermal optimal circular ring width of nearly zero. Hydraulically optimal is an inner to outer pipe radius ratio of 0.65 for turbulent and 0.68 for laminar flow types. In contrast, in this study, flow conditions in the circular ring are kept constant (a set of fixed Reynolds numbers) during optimization. This approach ensures fixed flow conditions and prevents inappropriately high or low mass flow rates. The optimization is carried out for three objectives: Maximum energy gain, minimum hydraulic effort and eventually optimum net-exergy balance. The optimization changes the inner pipe radius and mass flow rate but not the Reynolds number of the circular ring. The thermal calculations base on Hellström’s borehole resistance and the hydraulic optimization on individually calculated linear loss of head coefficients. Increasing the inner pipe radius results in decreased hydraulic losses in the inner pipe but increased losses in the circular ring. The net-exergy difference is a key performance indicator and combines thermal and hydraulic calculations. It is the difference between thermal exergy flux and hydraulic effort. The Reynolds number in the circular ring is instead of the mass flow rate constant during all optimizations. The result from a thermal perspective is an optimal width of the circular ring of nearly zero. The hydraulically optimal inner pipe radius is 54% of the outer pipe radius for laminar flow and 60% for turbulent flow scenarios. Net-exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains. The exact result depends on the earth’s thermal properties and the flow type. Conclusively, coaxial geothermal probes’ design should focus on the hydraulic optimum and take the thermal optimum as a secondary criterion due to the dominating hydraulics.

Exergetic Evaluation of Steel Coaxial Heat Exchangers

Background: A proven option to found buildings are geothermally activated steel pipes. Statics determine their dimensions. Energy improvement research focuses on the radius of inner pipe of such coaxial geothermal probes. Mass flow rate is often constant when optimizing inner pipe dimensions. In contrast, in this study flow conditions in outer pipe are constant (constant Reynolds number) to ensure that they not change during optimization. Aim is to maximize net exergy difference for the desired flow type by changing inner pipe radius (after deduction of hydraulic effort). System technology can be selected based on this optimal design and its associated boundary conditions for mass flow and temperatures.Methods: Thermal calculations based on Hellström are carried out to quantify an influence of changing inner pipe radius on thermal yield. A hydraulic optimization of inner pipe radius is performed. Increasing inner pipe radius results in decreasing hydraulic losses in inner pipe but increases hydraulic losses in outer circular ring. Net exergy difference is a key performance indicator to combine thermal and hydraulic effects. Optimization of net exergy difference is carried out for selected scenarios. All calculations are based on various, but fixed Reynolds numbers in the circular ring (Re = [4e3; 1e4; 1e5]), instead of fixed mass flow rates. This ensures fixed flow conditions and no unnecessary high mass flow rate.Results: Optimal inner radius is approximately as large as outer radius considering thermal results. Reynolds numbers are always bigger in inner pipe, due to the constant Reynolds number in circular ring. Both indicate that from a thermal point of view, a high mass flow rate and a high degree of turbulence are particularly important. Hydraulic optimal inner pipe radius is 54% of outer pipe radius for laminar flow scenarios and 60% for turbulent flow scenarios. Exergetic optimization shows a predominant influence of hydraulic losses, especially for small temperature gains.Conclusions: Design of coaxial geothermal probes should focus on the hydraulic optimum and take energetic optimum as a secondary criterion to maximize net exergy difference.

Theoretical Analysis of Fractional Viscoelastic Flow in Circular Pipes: General Solutions

Fractional calculus is a relatively old yet emerging field of mathematics with the widest range of engineering and biomedical applications. Despite being an incredibly powerful tool, it, however, requires promotion in the engineering community. Rheology is undoubtedly one of the fields where fractional calculus has become an integral part of cutting-edge research. There exists extensive literature on the theoretical, experimental, and numerical treatment of various fractional viscoelastic flows in constraint geometries. However, the general theoretical approach that unites several most commonly used models is missing. Here we present exact analytical solutions for fractional viscoelastic flow in a circular pipe. We find velocity profiles and shear stresses for fractional Maxwell, Kelvin–Voigt, Zener, Poynting–Thomson, and Burgers models. The dynamics of these quantities are studied with respect to normalized pipe radius, fractional orders, and elastic moduli ratio. Three different types of behavior are identified: monotonic increase, resonant, and aperiodic oscillations. The models developed are applicable in the widest material range and allow for the alteration of the balance between viscous and elastic properties of the materials.

ANALISIS TEGANGAN PADA ELBOW PIPE SA 123 Gr.T22 DI SHELL AND TUBE HEAT EXCHANGER

Heat exchanger is a system used to transfer heat between fluids. The most cases of heat exchanger failure is leakage pipe. This study aims to see the effect of increasing the radius of the elbow pipe in the shell and tube heat exchanger on the stress due to internal and external pressure. The research using ANSYS 15 at elbow pipe radius 40 mm, 51 mm and 62 mm with internal pressure 20.4 MPa and external pressure 2.04 MPa. Obtained maximum results occur in 40 mm radius elbow pipe of 81,528 MPa and minimum result occurs in 62 mm of 76,212 MPa. The stress that occurs in all elbow pipe can be said safe because the stress value is still under the pipe material yield point.

Radiation analysis of sound waves from semi-infinite coated pipe

An analytical solution is presented for the problem of radiation of sound waves from a semi-infinite circular cylindrical coated pipe which is partially lined from inside. By stating the total field in duct region in terms of normal waveguide modes (Dini’s series) and using the Fourier transform technique elsewhere, we obtain a Wiener–Hopf equation whose solution involving three sets of infinitely many unknown expansion coefficients satisfying three systems of linear algebraic equations. This system is solved numerically and the influence of some parameters (pipe radius, impedances, extension, etc.) on the radiation phenomenon is displayed graphically.

The three-dimensional structure of swirl-switching in bent pipe flow

Swirl-switching is a low-frequency oscillatory phenomenon which affects the Dean vortices in bent pipes and may cause fatigue in piping systems. Despite thirty years worth of research, the mechanism that causes these oscillations and the frequencies that characterise them remain unclear. Here we show that a three-dimensional wave-like structure is responsible for the low-frequency switching of the dominant Dean vortex. The present study, performed via direct numerical simulation, focuses on the turbulent flow through a $90^{\circ }$ pipe bend preceded and followed by straight pipe segments. A pipe with curvature 0.3 (defined as ratio between pipe radius and bend radius) is studied for a bulk Reynolds number $Re=11\,700$, corresponding to a friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\approx 360$. Synthetic turbulence is generated at the inflow section and used instead of the classical recycling method in order to avoid the interference between recycling and swirl-switching frequencies. The flow field is analysed by three-dimensional proper orthogonal decomposition (POD) which for the first time allows the identification of the source of swirl-switching: a wave-like structure that originates in the pipe bend. Contrary to some previous studies, the flow in the upstream pipe does not show any direct influence on the swirl-switching modes. Our analysis further shows that a three-dimensional characterisation of the modes is crucial to understand the mechanism, and that reconstructions based on two-dimensional POD modes are incomplete.

Process Planning for the Lateral Extrusion of a Pipe with a Lost Core

In this paper, the authors discuss process planning for the lateral extrusion of a pipe with a lost core. In this process, maximum longitudinal length of the bulged part is restricted by the balance of the extrusion speed of the material and the lost core. In the free bulging condition, longitudinal length is limited to the pipe radius, because the extrusion speed of the core is slower than that of the pipe material when the longitudinal length of the bulged part is longer. The authors designed a two-stage forming process using the transit shape of a truncated cone to solve this problem. The dimensions of the truncated cone were estimated through trial-and-error using a commercial FEM simulator and considering the stretch effect for wrinkles of the pipe by deformation and traveling of the lost core. Finally, the authors conducted experiments to confirm the design’s validity. As a result, a longer longitudinal length of the bulged part than the pipe radius was successfully obtained.

Development of Stress Intensity Factors for Cracks With Large Aspect Ratios in Pipes and Plates

The stress intensity factors (SIFs) for pipes containing semi-elliptical surface cracks with large aspect ratios were calculated by finite-element analysis (FEA). The cracks were circumferential and axial surface cracks inside the pipes. The parameters of the SIFs are crack aspect ratio, crack depth, and the ratio of pipe radius to wall thickness. In comparing SIFs for plates and pipes, it can be clarified that SIFs for both plates and thin pipes with t/Ri ≤ 1/10 are almost the same, and the SIFs for plates can be used as a substitute for pipes with t/Ri ≤ 1/10, where t is the pipe wall thickness, and Ri is the inner radius of the pipe. This means that it is not necessary to provide SIF solutions for pipes with t/Ri ≤ 1/10, and it is suggested that the number of tables for influence coefficient values for pipes can be significantly reduced.

Modal instability of the flow in a toroidal pipe

The modal instability encountered by the incompressible flow inside a toroidal pipe is studied, for the first time, by means of linear stability analysis and direct numerical simulation (DNS). In addition to the unquestionable aesthetic appeal, the torus represents the smallest departure from the canonical straight pipe flow, at least for low curvatures. The flow is governed by only two parameters: the Reynolds number $\mathit{Re}$ and the curvature of the torus ${\it\delta}$, i.e. the ratio between pipe radius and torus radius. The absence of additional features, such as torsion in the case of a helical pipe, allows us to isolate the effect that the curvature has on the onset of the instability. Results show that the flow is linearly unstable for all curvatures investigated between 0.002 and unity, and undergoes a Hopf bifurcation at $\mathit{Re}$ of about 4000. The bifurcation is followed by the onset of a periodic regime, characterised by travelling waves with wavelength $\mathit{O}(1)$ pipe diameters. The neutral curve associated with the instability is traced in parameter space by means of a novel continuation algorithm. Tracking the bifurcation provides a complete description of the modal onset of instability as a function of the two governing parameters, and allows a precise calculation of the critical values of $\mathit{Re}$ and ${\it\delta}$. Several different modes are found, with differing properties and eigenfunction shapes. Some eigenmodes are observed to belong to groups with a set of common characteristics, deemed ‘families’, while others appear as ‘isolated’. Comparison with nonlinear DNS shows excellent agreement, confirming every aspect of the linear analysis, its accuracy, and proving its significance for the nonlinear flow. Experimental data from the literature are also shown to be in considerable agreement with the present results.