Piston Phase Research Articles

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.

Calculation and correction of piston phase aberration in synthesis imaging

The principle of redundant spacings calibration has previously been described for the purpose of calibrating piston phase aberration affecting elements of a dilute aperture array using a system of linear equations in terms of the aperture phases as well as object phase information. Here we develop matrices for the correction of piston phase aberration by use of image sharpness and also by phase retrieval. These are both presented in wavefront sensor formulation in order to draw analogy between the approaches. We then discuss solution ambiguity affecting both methods and describe array design criteria to prevent such ambiguity. The problem of increased image aliasing under image sharpness correction is also highlighted.

Sub-aperture piston phase diversity for segmented and multi-aperture systems

Phase diversity is a method of image-based wavefront sensing that simultaneously estimates the unknown phase aberrations of an imaging system along with an image of the object. To perform this estimation a series of images differing by a known aberration, typically defocus, are used. In this paper we present a new method of introducing the diversity unique to segmented and multi-aperture systems in which individual segments or sub-apertures are pistoned with respect to one another. We compare this new diversity with the conventional focus diversity.

Atmospheric Phase Error in Coherent Laser Radar

Coherent laser radar (ladar) deduces the shape, velocity and vibration of a remote target by measuring the round-trip optical phase or the Doppler shift of target-scattered light. Phase fluctuations from wind-driven atmospheric turbulence generate micro-Doppler or velocity error at mum/sec levels. The turbulence-induced noise spectra of all geometric phase components of the ladar, the average phase power spectral densities of arbitrary ladar receiver modes, and the resultant Doppler noise spectra, are derived in the Rytov approximation for any isotropic stationary turbulence, any wind velocity profile, any Fresnel number and any source illumination pattern. In Kolmogorov turbulence the piston phase noise spectrum, and the average phase shift over a time interval, are well-approximated by simple universal asymptotic forms dependent only on atmospheric coherence length, turbulence-weighted average wind speed Vmacr, and aperture size D. The spectrum slope changes at a critical frequency of order Vmacr/D. The approximate results do not depend on the usually-unknown outer scale of turbulence

Basic Limitations on the Performance of Stirling Engines

Abstract The performance of Stirling engines is subject to limitations resulting from power dissipation in the regenerator. The dissipation is caused by pressure gradients in the regenerator required to generate flow. Without this flow the power output would be zero. Hence the dissipation is an essential element of the operation of the engine. Using linearized theory, the pressure in the compression and expansion spaces is found as a function of the ratio of piston amplitudes and piston phase difference. The regenerator is taken to be thermally perfect. All variations are taken to be sinusoidal in time. Expressions are derived for the dimensionless power output and the thermal efficiency at a given amplitude of the compression piston. Upper bounds on the power output and the efficiency are found as function of frequency and of regenerator void volume. Special attention is given to the case of piston amplitude ratio equal to 1.

A06 ロス・ヨーク機構の解析と応用(スターリングエンジン及び関連要素と応用システム(2))

Ross-Yorke drive mechanism is composed by the crank disk, the T-type link, the support link and becomes the structure to work a piston using each connecting rod from the side P_h of the T-link expansion piston and the P_c of the side of the compression piston. In this report, it did and it investigated a simulation analysis by this Ross-Yorke drive mechanism about the estimation method in the phase angle and the estimation method of the piston stroke. Moreover, it investigates about transformation Ross-Yorke drive mechanism that a different piston stroke is gotten, too. As a result, we were able to propose the new equation of the experiment of the piston stroke and phase angle.

A thermodynamic study for the optimization of stable operation of free piston Stirling engines

One of the most novel applications of the Stirling cycle is in the free piston configuration that was initially designed by W. Beale. In free piston Stirling engines (FPSEs), there are no mechanical linkages coupling the pistons or displacers, the motions of the reciprocating components follow the working gas pressure variations. Fillipo de Monte and G. Benvenuto have recently proposed a linearization technique of the dynamic balance equations. The aim of this paper is to predict the thermodynamic conditions for stable operation of FPSEs and their modeling. The equations of the angular velocity are solved analytically in terms of the working gas mass and the displacer–piston phase angle of the machine. Using the criterion of stable engine cyclic steady operation, a mathematically rigorous form is obtained for the main parameters of the engine. Furthermore, for simplicity reasons, thermodynamic magnitudes are obtained using the Schmidt analysis (isothermal model).

An Experimental Study on a Three-Temperature Three-Cylinder Stirling Cycle Machine

A new general three-temperature three-cylinder Stirling cycle machine designed by vector analysis reported before has been manufactured and experimented. The machine has three cylinders (Hot, Middle and Cold temperature) and the phase angle of the Hot piston can be changed between 80 and 160 degrees to the Middle piston. The measured performance and the P-V diagrams of each cylinder in various experiments are shown to agree well with the predicted values by vector analysis. Also, the change of performance of each cylinder by Hot piston phase change is qualitatively similar to the theoretical one. Moreover, applications of this kind of machine are reported.

Algebraic reconstruction of a small-scale wave front

We show that a small-scale wave front can be reconstructed by an algebraic procedure from its intensity distribution in the focal plane, except for the ambiguities of the piston phase and the point-symmetrical solution of the complex conjugate. Details of the reconstruction procedure for a 3 x 3 wave front are presented, and the effectiveness of this procedure for a contaminated case is shown by computer simulation. A method for overcoming the ambiguity problem resulting from the point-symmetrical solution is also suggested.

Numerical Analysis of Stirling Engine. 3rd Report, Investigation of Engine Particulars.

For the purpose of predicting and evaluating of the Stirling engine performance in detail, the cycle simulation code requires a technique for the 3rd-order method. The first paper presented our code which was useful in the research and development of our Stirling engine NS 30 S. In the second paper, a comparative study of working gases (helium and hydrogen) was carried out, and the effect of the test conditions of temperature was investigated. In addition, the calculated results were inspected in comparsion with the experimental ones This paper describes the test conditions of pressure and the cylinder volume and the piston phase angle affecting the Stirling engine performance and design. Then, the particulars of heat exchangers are evaluated as to design optimization. As a result, it is verified that our code is an available tool for optimizing the Stirling engine design.

Friction Characteristics for Starting and Low-Speed Conditions of a Ball Joint in a Swashplate-Type Axial Piston Motor.

It has become very important to improve hydraulic motor efficency, especially in the starting and low-speed ranges, for finer hydraulic operation. From this point of view, this report aimed to provide technical data to help improve a swashplate-type axial piston motor's performance, particularly concerning the friction characteristics of a ball joint. The effects on its friction characteristics are experimentally examined with regard to swashplate angle, supply pressure, surface roughness, and friction coefficient, etc. The results show that the friction moment of a ball joint is almost never affected by the piston phase angle, and oil temperature, but depends heavily on supply pressure, and that the friction moment strongly affects oil film thickness and leakage flow.

Friction and Leakage Characteristics between the Valve Plate and Cylinder for Starting and Low-Speed Conditions in a Swashplate-Type Axial Piston Motor.

Improvement of the efficiency of hydraulic motors is very important issue, especially in the starting and low-speed range, for finer hydraulic operation. From this point of view, this report aimed to provide technical data to help improve the swashplate-type axial piston motor performance, particularly in terms of friction, leakage characteristics and oil film thickness between the valve plate and cylinder. The effects on these characteristics are examined with regard to supply pressure, rotational speed, and static force balance. The following results were obtained: (1) friction torque between the valve plate and cylinder is almost never affected by rotational speed or piston phase angle, but strongly depends on supply pressure and static force balance; (2) leakage flow rate is affected by supply pressure, rotational speed and static force balance.

Study on the heat transfer of heat exchangers for the Stirling engine. 1st Report. Heat transfer in a heated tube under the reversing flow condition.

Heat transfer characteristics in heated tubes under the periodically reversing flow conditions have been experimentally investigated using the test apparatus that simulates heat exchangers for the actual Stirling engine. It is shown that the heat transfer characteristics under these conditions are greatly affected by the piston phase difference that generates the reversing flow of working fluid, and this phenomena is proper to the heat transfer under the periodically reversing flow which is different from the conventional convective heat transfer in the steady flow. The experimental correlation for the heat transfer coefficient on these conditions is induced by the use of the working gas velocity evaluated from the Schmidt cycle model that is one of the ideal Stirling cycles concerning the influence of the piston phase difference.

Effect Of Piston And Tilt Bias Errors In Multiple Wavefront Interference

The impact of tilt bias errors in multiple wavefront interferometry is assessed in terms of its effect on the ability to determine piston phase differences between wavefronts from such interferometry. The error in such piston phase determination due to tilt bias has been found to be substantial. On the other hand, several techniques have been found to be viable in which both tilt and piston phase errors may be determined simultaneously from such interferometry with proper algorithms.

Phased Array System Using The Far-Field Point Spread Function

We present a description of a phased array system using the far-field point spread function to estimate the tilt and piston errors. Digital control electronics were utilized to phase one beam to two others that were already in phase to simulate a multiple-aperture telescope system. A control algorithm for estimation of tilt and piston errors similar to the Newton-Raphson algorithm for locating the roots of a function was implemented. A simulation of the system was performed, the system hardware was built, and the system was tested in both an off-line software test and an experimental test-bed. Piston phasing with a capture range of X/4 and closed-loop tilt phasing with a bandwidth of 2 Hz were accomplished.

Design Of A Wide Field Of View Phased Array Telescope

The design of the Multipurpose Multiple Telescope Testbed (MMTT) is described. The MMTT, whose construction is now nearly complete, is believed to be the first wide field of view phased array imaging telescope. The design philosophy and alignment requirements are discussed and the telescope is described. The array consists of four 20 cm telescopes and operates with visible light. The coherently combined image has a 30 arcmin field of view. A key design goal is the maintenance of lateral pupil geometry to within 1µm of the ideal. Two mirrors behind each afocal telescope combine the four beams into one and are actuated to control both tilt and piston. Together, the two beam combiner mirrors control lateral pupil geometry. A control system senses the lateral pupil geometry error by continuously measuring piston phase changes over the telescope field of view. A discrete time varying Kalman filter then processes these measurements to estimate lateral pupil geometry errors.

Optical misalignment sensing and image reconstruction using phase diversity

A segmented-aperture telescope such as the Multiple-Mirror Telescope will suffer from phase errors unless the segments are aligned to within a small fraction of a wavelength. Such a coherent alignment of the segments is difficult to achieve in real time. An alternative is to record the images degraded by phase errors and to restore them after detection by using phase-retrieval techniques. In this paper we describe the use of Gonsalves’s phase-diversity method (which was previously used to combat atmospheric turbulence) to correct imagery blurred by a misaligned segmented-aperture telescope. Two images are recorded simultaneously: the usual degraded image in the focal plane and a second degraded image in an out-of-focus plane. An iterative gradient-search algorithm finds the phase error of the telescope that is consistent with both degraded images. We refer to this technique as the method of multiple-plane measurements with iterative reconstruction. The final image is obtained by a Wiener–Helstrom filtering of the degraded image using the retrieved phase errors. The results of reconstruction experiments performed with simulated data including the effects of noise are shown for the case of random piston phase errors on each of six segments.

Analysis and performance prediction of electromagnetically-driven free displacer Stirling cryocooler

Abstract A new approach to determine the pressure fluctuations in the workspace of the free displacer Stirling cryocooler utilizing the modified form of correlation for flow friction factor has been adopted here. These equations of pressure fluctuations are used to solve the equation of motion of the free displacer resulting in equations of the amplitude of displacer motion and phase shift between piston and displacer motion. Applying the perfect gas law to the mass of gas in the regenerator, instantaneous pressure in the dead space is determined. Similarly, equations of the amplitude of piston motion and phase shift between piston and applied voltage have also been obtained. This analysis shows that the coefficient of performance of the perfect regenerative free displacer Stirling cryocooler is a function of the kinematic viscosity ratio instead of temperature ratio as in the case of Schmidt cycle analysis. The comparison of predicted performance using both Schmidt technique and this approach with experimental results are also presented.

A study on some periodically oscillating flows in a circular pipe (Experimental velocity distributions)

This paper describes experimental velocity distributions in a circular pipe for some periodically oscillating air flows produced by tow pistons with arbitrary phase differences including 180°. The following facts are found for experimental conditions having a Reynolds number Re=1.32×104-5.94×104 and a reduced frequency √(ω')=10.9-18.8. (1) The turbulence appears in velocity waves for all conditions independently of the piston phase difference. (2) The instantaneous velocity distributions become almost uniform in the centre region and look like those for the steady turbulent flow regardless of the piston phase difference. (3) The velocity near the pipe wall is comparatively large in the accelerating period and comparatively small in the decelerating period independently of the piston phase difference. (4) As the piston phase difference becomes smaller from 180°to 90°, the difference of the maximum velocity and the period becomes larger between the right running flow and the left running flow.

Intrinsic formation of narrow-line absorption systems in QSOs – I. The piston phase

Intrinsic formation of narrow-line absorption systems in QSOs – I. The piston phase