Stanton Number St Research Articles

Numerical study on heat transfer of Stirling engine heater tube with rectangular micro-ribs

Numerical simulations were carried out to study the heat transfer and friction characteristics for Stirling engine heater tubes with three-dimensional internal extended micro-rib. During the numerical simulations, phase angle in a cycle ranged from 0° to 360°. The results represent that the friction factor (f) increased with micro-rib length (L) and micro-rib height (H) for enhanced tube within the range of parameters in this study. For the micro-rib heat tube of L = 60 mm and H = 0.9 mm, the j was equal to 1.44 and the average Stanton number St was significantly improved up to 1.287 compared to smooth tube, the friction factor f was also increased by almost 2.32. The outlet pressure from 0.7 Mpa to 1 Mpa with the cosine change is presented as the phase angle increases. Therefore the benefits are apparent for micro-rib heat tube in Stirling engine.

Experimental investigation of effect of different tube row-numbers, fin pitches and operating conditions on thermal and hydraulic performances of louvered and wavy finned heat exchangers

Heat exchangers are used in air conditioners, heat pumps, marine, land and air vehicles, refrigeration systems, thermal and nuclear power plants, etc. Increasing heat transfer capacity of a heat exchanger means that the volume of the heat exchanger and the material used will be reduced. Besides, effects of some geometric parameters on heat transfer and pressure drop are more complex depending on the fin structure in fin and tube heat exchangers. In this study, three of the most dominant parameters affecting the thermal-hydraulic performance of a finned and tube heat exchanger were experimentally investigated. These are fin-type (louvered and wavy fins), fin pitch and number of tube-rows. The intermittent geometric structures of louvered fins break growing of the boundary layer and reduce its thickness yielding heat transfer enhancement. On the other hand, wavy fins cause an increase in the heat transfer area due to its large flow length and create instabilities in the flow due to flow separations increasing the heat transfer coefficient. In the present study, specifically five louvered finned and three wavy finned and round tube heat exchanger prototypes were manufactured. Heat transfer and pressure drop experiments of these heat exchangers were performed at a wind tunnel in a conditioned room. Heat transfer and pressure drop characteristics were presented as heat transfer coefficient ho, Stanton number St, Nusselt number Nu, dimensionless pressure drop coefficient Cp, Colburn-j factor, Fanning friction factor f, jlouver/jwavy, flouver/fwavy, j/f1/3 ratios and JF factor. The results were examined from the point of heat transfer and pressure drop mechanisms of louvered and wavy fins for the different number of tube-rows, fin pitches and air inlet velocities. It is found that Colburn-j factors and Fanning friction f factors of the LFRTHXs are higher than those of the WFRTHXs for all the studied cases. Colburn-j factors of the LFRTHXs are higher by 16.4–6.9%, 28.5–18.3% and 25–11.7% than those of the WFRTHXs for the cases of two tube-rows, three tube-rows and four tube-rows, respectively. On the other hand, pressure drops of the LFRTHXs are significantly higher than those of WFRTHXs. However, the thermal-hydraulic performances of the LFRTHXs are still higher than that of WFRTHXs. The thermal-hydraulic performance criteria j/f1/3 ratios of the LFRTHXs are higher by 9.6–4.1%, 22.1–16% and 16.8–7.4% than those of the WFRTHXs for the cases of two tube-rows, three tube-rows and four tube-rows, respectively.

Grid independence in the study of boundary layer and its application in Hypergolic Propellants

Numerical simulation and experimental validation of a hypersonic flat plate and isothermal turning wall flow were conducted in the current study. The investigation was based on three kinds of grids (Grid1, Grid2, and Grid3) with laminar flow and three types of turbulence models (BL, SA, and SST). Under the same initiation and different turbulence models, the convergence process of the friction drag coefficient CP and the Stanton number St of a hypersonic flat plate flow revealed four results. First, the flow turbulence effect in the BL model simulation was responsive to CP and St. Second, the SA and SST model simulations both reflected the development process of flow turbulence. Third, the flow turbulence effect in the SST model simulation did not gradually emerge until the laminar flow simulation was sufficient. Moreover, the SA model simulation did not exist on such obvious hysteresis. Fourth, by comparing CP and St of a hypersonic flat-plate laminar simulation under the three grids, the errors of the calculation results of Grid2 and Grid3 were small.

Optimal performance of regenerative cryocoolers

The key component of a regenerative cryocooler is its regenerative heat exchanger. This device is subject to losses due to imperfect heat transfer between the regenerator material and the gas, as well as due to viscous dissipation. The relative magnitudes of these losses can be characterized by the ratio of the Stanton number St to the Fanning friction factor f. Using available data for the ratio St/ f, results are developed for the optimal cooling rate and Carnot efficiency. The variations of pressure and temperature are taken to be sinusoidal in time, and to have small amplitudes. The results are applied to the case of the Stirling cryocooler, with flow being generated by pistons at both sides of the regenerator. The performance is found to be close to optimal at large ratio of the warm space volume to the regenerator void volume. The results are also applied to the Orifice Pulse Tube Refrigerator. In this case, optimal performance additionally requires a large ratio of the regenerator void volume to the cold space volume.

Genetic algorithm based correlations for heat transfer calculation on concave surfaces

Laboratory experiments were carried out on a boundary layer over a concave wall subject to Görtler instability in the presence of forced wavelengths. Measurements of the local heat transfer along the concave wall permit calculation of the local Stanton number St for various axial positions x, nominal velocity U n , the wavelength λ and strength d w of the forced initial perturbations. The relation among these variables was constructed by a phenomenological argument in the form of classical power law correlations: St = a ( Re θ ) b x R c λ θ d . Correlations constants are then derived by genetic algorithm methods. The calculated Stanton number is in good agreement with the experimental results. In this paper we propose correlations for the calculation of heat transfer on concave surfaces (such as gas turbine blade pressure side) where the flow is complex due to the presence of streamwise vortices.

Optimal regenerator performance in Stirling engines

The key component of a Stirling engine is its regenerative heat exchanger. This device is subject to losses due to dissipation arising from the flow through the regenerator as well as due to imperfect heat transfer between the regenerator material and the gas. The magnitudes of these losses are characterized by the Stanton number St and the Fanning friction factor f, respectively. Using available data for the ratio St/f, results are found for the Carnot efficiency and the power output of the regenerator. They depend on the conductance and on the ratio of pressures at the two sides of the regenerator. Optimum results for efficiency and power output of the regenerator are derived in the limit of zero Mach number. The results are applied to the Stirling engine. The efficiency and the power output of the engine are found for given amplitude of the compression piston. Optimization with respect to regenerator conductance and piston phase angle leads to a maximum possible value of the power output. Under optimal conditions, the Carnot efficiency just below this maximum is close to 100%. Copyright © 2009 John Wiley & Sons, Ltd.

A Lumped Parameter Heat Transfer Analysis for Composting Processes With Aeration

A Lumped Parameter Heat Transfer Analysis for Composting Processes With Aeration

Drag Coefficient and Stanton Number Behavior in Fluid Flow Across a Bundle of Wing-Shaped Tubes

Transient numerical simulations of fluid and heat flow were performed for eight heat exchanger segments with cylindrical and wing-shaped tubes in staggered arrangement. Their hydraulic diameters dh were from 0.5824 to 3.899cm for the cylindrical tubes, and from 0.5413 to 3.594cm for the wing-shaped tubes. Based on the recorded time distributions of velocity uf(t) and temperature Tf(t), time average Reynolds number Re¯, drag coefficient C¯d, and Stanton number St¯ were calculated. In general, the drag coefficient and the Stanton number are smaller for the wing-shaped tubes than for the cylindrical tubes. However, with an increasing hydraulic diameter, these differences between both forms of tubes diminish. The time average values were further used to construct the drag coefficient and the Stanton number as polynomial functions C¯d(dh,Re¯) and St¯(dh,Re¯).

Permselectivity of calcium ion to potassium ion in ion exchange membrane electrodialysis of sugar solution

The permselectivity of calcium ion relative to potassium ion, T Ca K , in sugar solution has been studied with an electrodialyzer which consists of eleven pairs of anion exchange membranes, Selemion AMV, and cation exchange membranes, Selemion CMV. The experimental results show that T Ca K decreases as the current density and the equivalent ratio of potassium ion to calcium ion, R, increase, and increases as the flowrate and the total concentration of diluent increase, but is independent of the sugar concentration of the diluent. By means of dimensional analysis and correlation of the experimental results, T Ca K is found to be a function of Stanton number St and the feed ion ratio R, and can be expressed by the equation T Ca K = 0.0119 × St − 0.85 R − 1.18 . The results also indicate that T Ca K appraoches (Z Ca /Z K )(Ū Ca /Ū K )α Ca K and (D Ca /D K ) [(Z Ca − Z Cl /(Z K − Z Cl ) ] as the current density approaches zero and the limiting current density, respectively.

A study on the transport behavior of cations in ion exchange membrane electrodialysis

The permselectivities of cations in ion exchange membrane electrodialysis for NaCl-MgCl 2 and NaCl-CaCl 2 systems are investigated. The experimental results show that the permselective coefficients T Mg Na and T Ca Na decrease as the current density increases, but increase as the bulk velocity and the total equivalent concentration of diluent increases at constant temperature. It also indicates that the permselectivity is independent of the composition of diluent at constant current density, temperature, flow rate and total equivalent concentration of diluent. The correlation of experimental results shows that the empirical relation between permselective coefficient and Stanton number St can be expressed by the following equations: T Mg Na = 1.527 St -0.51 as 0.23 × 10 -3 < St < 0.9 × 10 -3 and T Mg Na = 1.05 as St > 0.9 × 10 -3 for NaCl-MgCl 2, system; and T Ca Na= 1.412 St -0.403 as 0.4 × 10 -3 < St < 2 × l0 -3 and T Mg Na = 1.185 as St > 2 × 10 -3 for NaCl-CaC1 2 system. The result also indicates that the permselective coefficient T B A decreases and approaches to the value of the ratio of the ionic mobility U B/ U A as Stanton number increases.

PREFERENTIAL ION TRANSPORT THROUGH ION EXCHANGE MEMBRANES BY ELECTRODIALYSIS

The preferential transport of a certain ionic species to others through an ion exchange membrane has been investigated. It was found from some experimental data that the preferential ion transport, SBA, should be closely related to an operating parameter ξ, where SK+NA+ for example, is defined as the ratio of the Sherwood number concerning the transfer rate of K+ to that of Na+, and E is defined as (∧Δφ/2FDV). The Stanton number St=(l/F)/C10V defined as the ratio of the total ionic flux in the direction to the membrane to that in the direction of the bulk flow, was also a function of ξ. These factors, ∧, Δφ, F, D, V, I, and C10 are the equivalent conductivity, the effective applied voltage to a single desalting compartment, the Faraday constant, the channel thickness, the linear flow velocity, the current density and the total equivalent concentration, respectively. Under the operating condition of ξ> IO-3, no ion exchange membrane will serve to transport a certain ion preferentially. If ξ∧1O-4, however, the membrane will fully reveal its own ability for selecting a certain ionic species, because the concentration ratio of two ionic species at the membrane surface will approach that in the equilibrium state.

Turbulent heat transfer and temperature profiles in a rifled pipe

Turbulent temperature profiles and heat transfer coefficients have been measured in an electrically heated 2 in. i.d. pipe with a 1 4 × 1 4 in, spiral rib of pitch/dia. ratio 2·58. Rifling resulted in greater than twofold increases in Stanton number St, but with a proportionate increase in friction factor C F , which is dependent on Re. Logarithmic plots of St/C F against Re show the rifled tubes to be generally less efficient than smooth tubes, although the efficiencies for air are considerably closer together than those for water. Dimensionless temperatures t + were obtained and show the temperature profile to be almost flat in the turbulent core for both water and air. This is consistent with the greater relative efficiency for air since proportionately more of the resistance is found in the turbulent core with fluids of low Prandtl number. These results suggest that rifled tubes might be used to ensure uniform radial temperatures in tubular reactors.