Cross-flow Tube Research Articles

Analytical-numerical method for calculating cross-flow tube heat exchangers considering temperature-dependent fluid heat capacities

The paper presents a mathematical model of a steam reheater in a steam boiler installed in a power unit of 1000 MW. A new numerical-analytical method was used to determine the temperature distribution of steam, flue gas, and the reheater’s tube walls. The reheater is a two-pass cross-current heat exchanger. There are 44 panels of tubes on the width of the boiler. The steam flows parallel through 20 pipes in each pass. An analytical model of the superheater was developed with the assumption of the constant physical properties of steam and flue gas. The results of steam and flue gas temperature calculations obtained by the proposed method were compared with the exact method’s results. Very high accuracy of estimates was attained even if the whole superheater is divided into a few control volumes. The results of the first and second pass steam temperature calculations were compared using the P-NTU (Effectiveness - Number of Transfer Units) method. A perfect match between the steam temperature and the average temperature of the flue gas at the outlet of the reheater was found. The advantage of the developed method of superheaters modeling is the possibility to model heat exchangers with complex flow systems. The calculations were also carried out for temperature-dependent physical properties of steam and flue gas.

New analytical-numerical method for modelling of tube cross-flow heat exchangers with complex flow systems

A new method for thermal calculations of cross-flow tube heat exchangers was proposed. The heat exchanger is divided into finite volumes, inside which the fluid temperatures are given by analytical formulas. The advantage of the semi-analytical method developed is that the temperature inside the finite volume can be determined at any point, unlike the finite difference method widely used in exchanger heat modelling. Even when dividing the entire tube in one heat exchanger pass into a few finite volumes, e.g. into three segments, satisfactory results are obtained. By dividing the whole heat exchanger into a small number of finite volumes, the computer calculation time of heat exchangers with complicated tube arrangement is very short. The proposed method can be used to calculate heat exchangers with a complicated flow system in which the physical properties of fluids depend on temperature. Analytical and numerical models were developed for one and two pass finned tube heat exchangers to assess the accuracy of the proposed method. A two-pass car radiator mathematical model with two rows of tubes using the proposed method was developed. The results of the car radiator and steam reheater calculations are in good agreement with the analytical or experimental results.

Comparative analysis of the latest improvements in heat transfer and hydrodynamic characteristics of smooth tubes in cross flow

Comparative analysis of the latest improvements in heat transfer and hydrodynamic characteristics of smooth tubes in cross flow

New calculation method for tube cross-flow heat exchangers

A new method for thermal calculations of the cross-flow tube heat exchangers was proposed. The temperature of both fluids and the wall temperature are determined. The heat exchanger is divided into control volumes, in which outlet fluid temperatures are calculated by closed analytical formulas. Two examples of the application of the method for the calculation of two-pass cross-co-current and cross-countercurrent superheaters were presented. An exact analytical model was also developed for both superheaters to estimate the accuracy of the proposed method. The results of the superheater calculations using the developed method are in good agreement with the results obtained by the exact analytical models. The proposed method can be used to calculate heat exchangers with a complicated flow system in which the physical properties of fluids are temperature-dependent.

Numerical analysis for thermo-hydraulic performance of staggered cross flow tube bank with longitudinal tapered fins

Cross flow tube bank is an important constituent in most of the industrial heat exchanging systems such as Heating Ventilation and Air Conditioning (HVAC) systems, Waste Heat Recovery systems and Industrial Boilers. Considering the depletion of fossil fuels and allied environmental concerns, there is a huge need for improving the performance of the cross flow tube bank. The present numerical study investigates the effect of longitudinal taper fins on external flow over staggered cross flow tube bank. The longitudinal fins of various length (0.50 ≤ L/D ≤ 1.50), base thickness (0.40 ≤ T/D ≤ 0.80) and end thickness (t/D = 0.12 and 0.28) are used to evaluate the thermal performance of the tube bank. The thermal hydraulic performance is evaluated considering the effects on rate of heat transfer along with pressure drop characteristics across the tube bank. The results shows that the use of longitudinal taper fins significantly enhances the thermal hydraulic performance of cross flow tube banks. Moreover, the increase in length of fin results in an appreciable enhancement in Nusselt number, which overrules the increase in pressure drop penalty. Whereas, the increase in the fin base thickness, results in a significant reduction in pressure drop capable of compensating the reduction in Nusselt number. Hence, increase in both these dimensions results in higher thermal hydraulic performance than the bare tube bank. On the other hand, fin end thickness plays only a minor role in the finned tube bank performance. Lowering the value of fin end thickness slightly increase the thermal performance by suppressing the friction factor.

Experimental and numerical investigations for effect of longitudinal splitter plate configuration for thermal-hydraulic performance of staggered tube bank

The use of fins for the passive mode of heat transfer enhancement is being used since decades. The use of fin increases the rate of heat transfer by increasing the effective area available for the energy exchange. Hence, most of the modern heat exchanger makes use of different types of the fins to make the device more efficient and compact. Most of the fin configuration used in the heat exchanger not only increases the rate of heat transfer but also causes an undesirable rise in pumping power owing to the additional air/fluid resistance encountered. In the present study, longitudinal fins in the form of a splitter plates are used for the experimental study in case of a staggered cross flow tube bank. The splitter plate geometric configuration such as splitter plate length (0.50 ≤ L/D ≤ 1.50) and plate thickness (0.04 ≤ t/D ≤ 0.20) are varied to further enhance the overall thermal hydraulic performance of the tube bank. The three-dimensional numerical study is also performed for better fluid flow visualization. The use of the splitter plate with L/D = 1.0 and t/D = 0.20 improves the Nusselt number with the reduction in the overall pressure drop for most of the configuration, resulting in an improvement in the thermal-hydraulic performance of tube bank. Moreover, statistical correlations are developed for the Nusselt number and friction factor characteristics for longitudinally finned tube bank for the entire range of Reynolds number from 5000 to 25000.

Experimental investigation of the heat transfer for non-circular tubes in a turbulent air cross flow

ABSTRACT The purpose of this experimental study is to measure the drag and heat transfer coefficients of the non-circular tubes including square, elliptic, and cam-shape tubes in a turbulent air cross flow. Studies have been made at 0° to 180° angles of attack () and Reynolds numbers (Re) based on the equivalent diameter of a circular tube within the range of 1.4 × 104 < Reeq < 7.5 × 104. The equivalent diameter Deq = 46 mm was chosen for the tubes. The results show that the minimum and maximum drag coefficients (Cd) belong to the cam-shape and square tubes at 0°, respectively. The (Cd) of the cam-shape and square tubes are 60% less and 25% more than the equivalent circular tube, respectively. Also, the ratio of the average Nusselt number () to the drag coefficient, /Cd, was used to compare non-circular tubes and with their equivalent circular ones. The results show that the maximum value belongs to the cam tube and the minimum occurs for the square tube at α = 0°. The /Cd ratio of the cam tube is 128% more than the equivalent circular tube, while the square tube yields a /Cd ratio that is13% less than its circular equivalent.

The Recirculation Zone Characteristics of the Circular Transverse Jet in Crossflow

Transverse jets in crossflow are widely used in energy systems, especially as dilution air jets, fuel/air mixers, and combustion equipment, and have received extensive attention and plenty of research. However, the studies of the circular transverse jet issued from a circular gap at the circumferential direction of a tube in crossflow are very limited. This paper studies a relatively new jet: the circular transverse jet. Firstly, numerical calculations are conducted under different turbulence models but with the same boundary conditions. By comparing the numerical results of different turbulence models with the existing experimental data, the turbulence model which is most suitable for the numerical calculation of the circular transverse jet is selected. Then, this turbulence model is used to calculate and analyze the flow field structure and its characteristics. It is found that due to the aerodynamic barrier effect of the high-velocity jet, a negative pressure zone is formed behind the jet trajectory; the existence of the negative pressure zone causes the formation of a vortex structure and a recirculation zone downstream the circular transverse jet; and the length/width ratio of the recirculation zone does not change with the changes of the crossflow and the jet parameters. It means that the recirculation zone is a fixed shape for a definite device. This would be fundamental references for the studying of fuel/air mixing characteristics and combustion efficiency when the circular transverse jet is used as a fuel/air mixer and stable combustion system.

Enhanced thermal and fluid flow performance of cross flow tube bank with perforated splitter plate

ABSTRACT The cross flow over the tube bank is extensively employed in the heat exchangers. The present study investigates the heat transfer and frictional losses of cross flow tube bank with solid and perforated splitter plates. The experimental data are collected for bare tube bank, tube bank with solid and perforated splitter plate by varying the splitter plate width ratio (Rw) and the perforation index (Pi) in the Reynolds number range of 10,500–40,500. The cylindrical tube bank with perforated splitter plate having (Rw) of 0.5 and (Pi) of 1.5 yields maximum thermal and hydraulic performance.

Nonlinear Finite Element Analysis-Based Flow Distribution and Heat Transfer Model

A new strategy for fast, approximate analyses of fluid flow and heat transfer is presented. It is based on Finite Element Analysis (FEA) and is intended for large yet structurally fairly simple heat transfer equipment commonly used in process and power industries (e.g., cross-flow tube bundle heat exchangers), which can be described using sets of interconnected 1-D meshes. The underlying steady-state model couples an FEA-based (linear) predictor step with a nonlinear corrector step, which results in the ability to handle both laminar and turbulent flows. There are no limitations in terms of the allowed temperature range other than those potentially stemming from the usage of fluid physical property computer libraries. Since the fluid flow submodel has already been discussed in the referenced conference paper, the present article focuses on the prediction of the tube side and the shell side temperature fields. A simple cross-flow tube bundle heat exchanger from the literature and a heat recovery hot water boiler in an existing combined heat and power plant, for which stream data are available from its operator, are evaluated to assess the performance of the model. To gain further insight, the results obtained using the model for the heat recovery hot water boiler are also compared to the values yielded by an industry-standard heat transfer equipment design software package. Although the presented strategy is still a “work in progress” and requires thorough validation, the results obtained thus far suggest it may be a promising research direction.

Constructal design of multiscale elliptic tubes in crossflow

AbstractThe optimal configuration of two‐scale elliptic tubes in crossflow is found on the basis of the constructal design. The larger tubes are installed inside a domain of fixed length and height. In the same domain, smaller tubes are inserted between the larger tubes in the entrance region at the mid leading edge to leading edge distance of the larger tubes. The spacing between the larger tubes, the semiminor axis of the larger tubes, the major axis of the smaller tubes, and the semiminor axis of the smaller tubes are varied inside the domain freely to find the optimal configuration. There are two optimal configurations: one without the smaller tubes and the other with the presence of the smaller tubes. Both the larger and the smaller tubes are heated at a constant surface temperature. The flow is induced by a fixed pressure difference. The equations for steady, laminar, two‐dimensional, and incompressible flow are solved by finite volume method. In the absence of the smaller tubes, the range of Bejan number (dimensionless pressure drop) is , and in the presence of the smaller tubes, Bejan number is Be = 105. The range of the dimensionless larger tubes semiminor axis is 0.1 ≤ B ≤ 0.4. Air is used to cool the row of the tubes with Prandtl number equal to 0.7. The results show that for different semiminor axes of the larger tubes, the heat transfer rate is enhanced when the smaller tubes are placed between the larger tubes.

Experimental and numerical investigations of flow-induced vibration of tube arrays subjected to cross flow

Flow-induced vibration of tube array structures is a major concern in nuclear engineering. In this paper, the dynamical behavior of flexible tubes in cross flow is studied. A computational fluid dynamics (CFD) model is developed to investigate the interaction between flow perturbations and tube oscillations. The Large Eddy Simulation (LES) is validated and adopted in the simulations. The motion of tubes in different tube configurations (i.e., single tube, three in line tubes, normal square tube array, and normal triangle tube array with different pitch to diameter ratios) under different flow conditions are analyzed and compared by time trace, power spectral density (PSD), phase plane plot and Poincaré map. Experiments have been conducted using a flexible tube in a closed-loop piping system to compare with the CFD model predictions. It is found that tube undergoes vortex-induced vibration and then fluid elastic instability, limit-cycle oscillation occurs when the inlet flow velocity exceeds a critical point. The central tube in normal square tube array is the most stable among the three configurations. The critical pitch to diameter ratio of tube array under reduced velocity Ur = 6 is about 5.5. The experimental observations are in good agreement with the CFD predictions.

Maximization of heat transfer density from a vertical array of flat tubes in cross flow under fixed pressure drop using constructal design

AbstractThe density of heat transfer rate from a vertical array of flat tubes in cross flow is maximized under fixed pressure drop using constructal design. With the constructal design, the tube arrangement is found such that the heat currents from the tubes to the coolant flow easily. The constraint in the present constructal design is the volume where the tubes are arranged inside it. The two degrees of freedom available inside the volume are the tube‐to‐tube spacing and the length of the flat part of the tubes (tube flatness). The tubes are heated with constant surface temperature. The equations of continuity, momentums, and energy for steady, two‐dimensional, and laminar forced convection are solved by means of a finite‐volume method. The ranges of the present study are Bejan number (dimensionless pressure drop) (103 ≤ Be ≤ 105) and tube flatness (dimensionless length of the tube flat part) (0 ≤ F ≤ 0.8). The coolant used is air with Prandtl number (Pr = 0.72). The results reveal that the maximum heat transfer density decreases when the tube flatness decreases at constant Bejan number. At constant tube flatness, the heat transfer density increases as the dimensionless pressure drop (Bejan number) increases. Also, the optimal tube‐to‐tube spacing is constant, irrespective of the tube flatness at constant Bejan number.

Numerical studies on the near wall y+ effect on heat and flow characteristics of the cross flow tube bank

The use of passive mode of heat transfer enhancement are most commonly used for the performance improvement with conservation of conventional fuels. In recent times, to visualize the insight of fluid flow analysis, the numerical simulations are mostly preferred. The number of grid points present in the in the fluid domain near the wall governs the accuracy and precision of the numerical study. Hence in the present study, three different near wall grid systems are consider to evaluate its effect on Nusselt number friction factor for the staggered tube bank arrangements. It is reported that y+ as 10, insensitive to boundary layer effects at higher flow rate, while y+ as 1.0, and 0.10 are in close approximation.

Experimental investigation on heat transfer and pressure drop of internal flow in corrugated tubes

The operating conditions of the pre-heater zone of an automotive vehicle waste heat recover heat exchanger occurs in, or close to, the transitional flow regime. For such an application the use of corrugated tubes in a cross flow tube heat exchanger is of particular interest. However, not much work has been done in the transitional flow regime in corrugated tubes where the internal flow changes from laminar to turbulent with heat transfer at high heat fluxes. Therefore, more data is needed. Hence, the main purpose of this work is the characterization of the heat transfer and pressure drop of internal flow in corrugated tubes. To this end an experimental setup was developed and validated for the study of a smooth tube and two corrugated tubes that have an internal diameter of 5.75 mm and a heating length of 0.38 m. The experiments were conducted in laminar, transitional and turbulent regime, with Reynolds numbers in the range from 429 to 6212, under both adiabatic and diabatic flow conditions. The heat flux imposed on the tube wall ranged from 5.5 kW/m2 to 21.1 kW/m2. The flow was hydrodynamically fully developed at test section inlet. The results revealed that the friction factor of the corrugated tubes presented a smoother transition than in the case of the smooth tube, being the diabatic and adiabatic friction factor for the corrugated tubes quite similar from laminar to turbulent regime. The corrugated tubes are more effective under transitional flow regime. The highest heat transfer augmentation occurs at Re ≈ 2000, specifically, the Nusselt number augmentation (Nuc/Nus) increases up to 4.7 for the corrugated tube with helical pitch p = 6 mm and up to 3.8 for the corrugated tube with p = 12 mm.

A numerical prediction on heat transfer characteristics from a circular tube in supercritical fluid crossflow

Studies on fluids at supercritical pressure have been developed in a rapid-growth manner so that geometries are not restricted to circular tube. This paper is devoted to conduct a brief review of the recent main experiments on supercritical fluids such as CO2, water, R134a and n-decane, and to comment the findings. In addition, this paper discusses the probability of supercritical fluids flowing across tube bundles for the frequent use in shell-and-tube heat exchangers in supercritical power cycle systems. A numerical prediction of flow patterns and heat transfer characteristics of a circular tube in supercritical water crossflow is carried out to make a fundamental investigation of the application of supercritical fluids on external flows. Results indicate that the influence of heat flux on heat transfer in crossflow is similar with that for in-tube flows. The thermal physical properties significantly affect the heat transfer and the flow patterns also show unique characteristics with the change of boundary conditions.

Wear Analysis of Tube-Baffle Vibration Interaction in a Tube Bundle

Wear analysis has been carried out on aluminum tube in parallel triangular tube bundle with P/D ratio of 1.45 and the baffle plate placed at the mid-span of the bundle. The cross-flow velocity of water ranges from 0.18 m/s to 0.55 m/s. For each flow velocity, tests were performed on five different flow velocities and three-time spans (tube-baffle interaction) i.e., 30, 60, and 90 min. The experiments were designed in a unique way to study the relationship between cross flow velocity and tube baffle interaction time with wear produced on the tube surface. This is the first study of its kind in which wear analysis of a flexible tube has been done in the water tunnel to simulate the real environment of the heat exchanger tubes. The vibration response of the monitored tube was acquired using a tri-axial wireless accelerometer. A Scanning Electron Microscope (SEM) was used for the measurement of wear sizes. It was observed that the transverse amplitude rises significantly at higher velocities as compared to streamwise amplitude results in significant wear in the transverse direction. The wear sizes also tend to increase with the cross-flow velocity and become prominent at higher velocities. A similar trend has been observed for the wear area and wears volume. Also with the increase in the tube-baffle interaction span, the wear scar tends to be deeper and wider significantly at higher velocities.

Comparison of LBM and CFD for Hydrodynamic Simulation of Cross-flow Tube Bundle

Comparison of LBM and CFD for Hydrodynamic Simulation of Cross-flow Tube Bundle

Numerical Simulation on Effect of Air Attack Angle on Wake and Vortex Formation for Tandem Elliptical Cylinders

The cross flow heat exchanger is used most commonly used in process heat transfer applications. The most commonly used tube geometry is a circular tube. However elliptical tube section is prominently used in recent times due to streamline tube profile. The present work is on elliptic tubes in cross flow with different attack angle from 0° to 90°. The effect of oncoming fluid attack angle on boundary layer, wake and vortex formation at the tube downstream is studied at Reynolds number of 7000. The pumping power increases as the attack angle is increased from 0° to 90°, which increases the turbulence within tubes. The numerical simulation is performed in ANSYS 14.5 with RNG k-e turbulence model. The vortex formation also intensifies with the attack angle of the cross fluid. This increases the turbulence and pressure drop with the tubes which is not desirable. The pumping power is relatively low at the lower attack angle of the air but increases drastically above at 60° and above angles. The attack angle up to 30° is recommended by considering the heat transfer enhancement and pumping power both for the present study.

Constructal design applied to elliptic tubes in convective heat transfer cross-flow of viscoplastic fluids

The objective of this work was to obtain geometries that maximize the heat transfer and minimize pressure drop for viscoplastic fluids in cross flow around elliptical section tubes. The Constructal Design associated with exhaustive search was employed to obtain the ellipse aspect ratios that maximize the Nusselt number and to minimize dimensionless pressure drop, for fixed parameters such as ellipse area, Reynolds (Re=1), Prandtl (Pr=1) and Herschel-Bulkley (HB=1) numbers. The viscoplastic fluid behavior was modeled using the Herschel-Bulkley constitutive equation. The power-law index, n, was a parameter to predict fluid shear thinning. The system of differential equations for flow and heat transfer was solved numerically by the finite volume method. The aspect ratio to maximize Nu‾, rq,opt, and the one to minimize Δp̃, rp,opt, were searched for different values of n, ranging from 0.4 to 1. The rq,opt was found to be very close to 1 for all n’s, which corresponds to the tube of circular cross section. Low aspect ratio tubes lead to the formation of greater unyielded zones as compared to high aspect ratio tubes. This may be a key to understand the increase in heat transfer from the tube as the aspect ratio increases to one. The aspect ratio that led to the lowest pressure drop was not the same for all fluids, contrarily to the behavior noticed for thermal purpose. It was noticed that as n decreases, the rp,opt, also decreases, meaning that to reduce pressure drop for more shear thinning fluids the tube must be slender. This may lead to the conclusion that elliptic tubes might be a good alternative in applications of heat transfer with mild viscoplastic fluids (low HB) only when there is the need to reduce pressure drop or pumping power.