Universality of low-energy scattering in three-dimensional field theory

a r X i v :c o n d -m a t /0108314v 1 [c o n d -m a t .s t a t -m e c h ] 20 A u g 2001Bethe Ansatz Solutions and Excitation Gap of the Attractive Bose-Hubbard ModelDeok-Sun Lee and Doochul KimSchool of Physics,Seoul National University,Seoul 151-747,KoreaThe energy gap between the ground state and the first excited state of the one-dimensional attractive Bose-Hubbard Hamiltonian is investigated in connection with directed polymers in random media.The excitation gap ∆is obtained by exact diagonalization of the Hamiltonian in the two-and three-particle sectors and also by an exact Bethe Ansatz solution in the two-particle sector.The dynamic exponent z is found to be 2.However,in the intermediate range of the size L where UL ∼O (1),U being the attractive interaction,the effective dynamic exponent shows an anomalous peak reaching high values of 2.4and 2.7for the two-and the three-particle sectors,respectively.The anomalous behavior is related to a change in the sign of the first excited-state energy.In the two-particle sector,we use the Bethe Ansatz solution to obtain the effective dynamic exponent as a function of the scaling variable UL/π.The continuum version,the attractive delta-function Bose-gas Hamiltonian,is integrable by the Bethe Ansatz with suitable quantum numbers,the distributions of which are not known in general.Quantum numbers are proposed for the first excited state and are confirmed numerically for an arbitrary number of particles.I.INTRODUCTIONThe dynamics of many simple non-equilibrium sys-tems are often studied through corresponding quantum Hamiltonians.Examples are the asymmetric XXZ chain Hamiltonian and the attractive Bose-Hubbard Hamilto-nian for the single-step growth model [1]and the directed polymers in random media (DPRM)[2],respectively.The single-step growth model is a Kardar-Parisi-Zhang (KPZ)universality class growth model where the inter-face height h (x,t )grows in a stochastic manner under the condition that h (x ±1,t )−h (x,t )=±1.The process is also called the asymmetric exclusion process (ASEP)in a different context.The evolution of the probability distri-bution for h (x,t )is generated by the asymmetric XXZ chain Hamiltonian [3].The entire information about the dynamics is coded in the generating function e αh (x,t ) .Its time evolution,in turn,is given by the modified asym-metric XXZ chain Hamiltonian [4–6],H XXZ (α)=−L i =1e 2α/L σ−i σ+i +1+12L i =1(b i b †i +1+b †i b i +1−2)−UL i =1b †ib i (b †ib i −1)4Lρ(1−ρ)and −n√4Lρ(1−ρ)≫1and the density of particles is fi-nite in the limit L →∞,∆(α)behaves as ∆(α)∼L −1.However,when α∆(α)∼L−3/2[3,11].The dynamic exponent z=3/2is a characteristic of the dynamic universality class of the KPZ-type surface growth.When the number of par-ticles isfinite and the density of particles is very low, it is known that∆(α)∼L−2[12].However,whenα<0,which corresponds to the ferromagnetic phase, most Bethe Ansatz solutions are not available althoughthe Bethe Ansatz equations continue to hold.Asαbe-comes negative,the quasi-particle momenta appearing inthe Bethe Ansatz equations become complex,so solutions are difficult to obtain analytically.The attractive Bose-Hubbard Hamiltonian is expected to have some resemblance to the ferromagnetic phaseof the asymmetric XXZ chain Hamiltonian consider-ing the equivalence ofαand−n.The equivalence isidentified indirectly by comparing the two scaling vari-ablesα LU under the relation U= 4ρ(1−ρ)or the two generating functions exp(αh(x,t) and Z(x,t)n under the relation Z(x,t)=e−h(x,t).In contrast to the asymmetric XXZ chain Hamiltonian,theBose-Hubbard Hamiltonian does not satisfy the Bethe Ansatz except in the two-particle sector[13].Instead, the attractive delta-function Bose-gas Hamiltonian,H D(n)=−1∂x2i−Ui<jδ(x i−x j),(4)which is the continuum version of the attractive Bose-Hubbard Hamiltonian,is known to be integrable by the Bethe Ansatz.The attractive delta-function Bose gas has been studied in Refs.[14]and[15].The ground-state energy is obtained from the Bethe Ansatz solution by us-ing the symmetric distribution of the purely imaginary quasi-particle momenta.However,the structure of the energy spectra is not well known for the same reason as in the asymmetric XXZ chain Hamiltonian withα<0. The unknown energy spectra itself prevents one from un-derstanding the dynamics of DPRM near the stationary state.In this paper,we discuss in Section II the distribu-tion of the quantum numbers appearing in the Bethe Ansatz equation for thefirst excited state of the attrac-tive delta-function Bose-gas Hamiltonian,the knowledge of which is essential for solving the Bethe Ansatz equa-tion.In Section III,the excitation gap of the attractive Bose-Hubbard Hamiltonian with a small number of par-ticles is investigated through the exact diagonalization method.We show that the gap decays as∆∼L−2,i.e., z=2,but that the exponent becomes anomalous when U∼L−1.The emergence of the anomalous exponent is explained in connection with the transition of thefirst excited state from a positive energy state to a negative energy state.The Bethe Ansatz solutions in the two-particle sector show how the behavior of the gap varies with the interaction.We give a summary and discussion in Section IV.II.QUANTUM NUMBER DISTRIBUTION FOR THE FIRST EXCITED STATEIn this section,we study the Bethe Ansatz solutions for the ground state and thefirst excited state of the attrac-tive delta-function Bose-gas Hamiltonian.The eigenstate of H D(n),Eq.(4),is of the formφ(x1,x2,...,x n)= P A(P)exp(ik P1x1+ik P2x2+···+ik P n x n),(5)where P is a permutation of1,2,...,n and x1≤x2≤...≤x n with no three x’s being equal.The quasi-particle momenta k j’s are determined by solving the Bethe Ansatz equations,k j L=2πI j+ l=jθ(k j−k l2+j,(j=1,2,...,n),(7)and the quasi-particle momenta are distributed symmet-rically on the imaginary axis in the complex-k plane. Care should be taken when dealing with thefirst excited state.For the repulsive delta-function Bose-gas Hamilto-nian,where U is replaced by−U in Eq.(4),the quantum numbers for one of thefirst excited states areI j=−n+12.(8)However,for the attractive case,by following the move-ment of the momenta as U changes sign,wefind that the quantum numbers for thefirst excited state should be given byI j=−n−12(=I1).(9)That is,the two quantum numbers I1and I n become the same.Such a peculiar distribution of I j’s does not ap-pear in other Bethe Ansatz solutions such as those for the XXZ chain Hamiltonian or the repulsive delta-function Bose-gas Hamiltonian.We remark that even though the two I j’s are the same,all k j’s are distinct;otherwise,the wavefunction vanishes.Such a distribution of quan-tum numbers is confirmed by the consistency between the energies obtained by diagonalizing the Bose-HubbardHamiltonian exactly and those obtained by solving the Bethe Ansatz equations with the above quantum num-bers for very weak interactions,for which the two Hamil-tonians possess almost the same energy spectra.When there is no interaction(U=0),all quasi-particlemomenta,k j’s,are zero for the ground state while for thefirst excited state,all the k j’s are zero except thelast one,k n=2π/L.In the complex-k plane,as the very weak repulsive interaction is turned on,the n−1momenta are shifted infinitesimally from k=0withk1<k2<···<k n−1,and the n th momentum is shifted infinitesimally to the left from k=2π/L.All the mo-menta remain on the real axis.When the interaction is weakly attractive,the n−1momenta become complexwith Im k1<Im k2<···<Im k n−1and Re k j≃0for j=1,2,...,n−1,and the n th momentum remains on thereal axis,but is shifted to the left.Figure1shows the dis-tribution of the quantum numbers and the quasi-particlemomenta in the presence of a very weak attractive in-teraction.The quasi-particle momenta are obtained by solving Eq.(6).Knowledge of the distribution of the quantum num-bers is essential for solving the Bethe Ansatz equations of the attractive delta-function Bose-gas Hamiltonian.For the original attractive Bose-Hubbard Hamiltonian,the Bethe Ansatz solutions are the exact solutions for the two-particle sector only,but are good approximate so-lutions in other sectors provided the density is very low and the interaction is very weak.This is because the Bethe Ansatz for the Bose-Hubbard Hamiltonian fails once states with sites occupied by more than three parti-cles are included.Thus,for the sectors with three or more particles,the Bethe Ansatz solutions may be regarded as approximate eigenstates provided states with more than three particles at a site do not play an important role in the eigenfunctions.In Ref.[13],it is shown that the error in the Bethe Ansatz due to multiply-occupied sites (occupied by more than three particles)is proportional to U2,where U(>0)in Ref.[13]corresponds to−U in Eq.(2).This applies to the attractive interaction case also.For the repulsive Bose-Hubbard Hamiltonian,the Bethe Ansatz is a good approximation when the density is low and the interaction is strong because the strong re-pulsion prevents many particles from occupying the same site[16].For the attractive Bose-Hubbard Hamiltonian, the Bethe Ansatz is good when the density is low and the interaction is weak because a weak attraction is better for preventing many particles from occupying the same site and because the error is proportional to U2.III.POWER-LA W DEPENDENCE ANDANOMALOUS EXPONENTWe are interested in the scaling limit L→∞with the scaling variable n√byE 0=−4sinh 2 κ2Lcosh2q 2L sinh2q2sinh κ−U,(12)andqL =logU +2cos(πU −2cos(π2s κ−s U,(14)which gives s κ≃1.151.When the size of the system L is increased by δL with U =U∗,the changes of κand q ,δκand δq ,are,from Eqs.(12)and (13),δκ=−πs κ(4s κ2−s U 2)L 2≡−πΓδL(4/π)s U −s U 2+4δLL 2.(15)The perturbative expansion ∆(L +δL )≃∆(L )(1−z (δL/L )),under the assumption that ∆(L )∼L −z ,gives the value of z effat U ∗:z eff=21+s κΓ+Σlog((L −1)/(L +1))(17)by using the solutions of Eqs.(12)and (13)for sufficiently large L .As discussed above,the exponent z effshows an anomalous peak near U =U ∗or UL/π=s U and ap-proaches 2.0as UL/π→0or ∞.Figure 6shows a plot of z effversus the scaling variable UL/πat L =10000.IV.SUMMARY AND DISCUSSIONAs the asymmetric XXZ chain generates the dy-namics of the single-step growth model,the attractive Bose-Hubbard Hamiltonian governs the dynamics of the DPRM.We studied the attractive Bose-Hubbard Hamil-tonian and its continuum version,the attractive delta-function Bose-gas Hamiltonian concentrating on the be-havior of the excitation gap,which is related to the char-acteristics of DPRM relaxing into the stationary state.For the attractive delta-function Bose gas Hamiltonian,The quantum numbers for the first excited state in the Bethe Ansatz equation are found for the attractive delta-function Bose gas Hamiltonian,and the distribution of the quasi-particle momenta is discussed in the presence of a very weak attractive interaction.Our result is the start-ing point for a further elucidation of the Bethe Ansatz solutions.We show that the excitation gap depends on the size of the system as a power law,∆∼L −z ,and that the exponent z can be calculated by using an exact diag-onalization of the attractive Bose-Hubbard Hamiltonian in the two-and the three-particle sectors and by using the Bethe Ansatz solution in the two-particle sector.The exponent z is 2.0.However,for the intermediate region where UL ∼O (1),the effective exponent z effshows a peak.The equivalence of the differential equations govern-ing the single-step growth model and DPRM implies some inherent equivalence in the corresponding Hamil-tonians.The power-law behavior of the excitation gap,∆∼L −2,for the attractive Bose-Hubbard Hamiltonian with a very weak interaction is the same as that for the asymmetric XXZ chain Hamiltonian with a small num-ber of particles,which is expected considering the rela-tion U =4ρ(1−ρ).The fact that the excitation gap behaves anomalously for U ∼L −1implies the possibility of an anomalous dynamic exponent z for a finite scaling variable n√[1]M.Plischke,Z.Racz,and D.Liu,Phys.Rev.B 35,3485(1987).[2]M.Kardar,Nucl.Phys.B 290[FS20],582(1987).[3]L.H.Gwa and H.Spohn,Phys.Rev.A 46,844(1992).[4]B.Derrida and J.L.Lebowitz,Phys.Rev.Lett.80,209(1998).[5]D.-S.Lee and D.Kim,Phys.Rev.E 59,6476(1999).[6]B.Derrida and C.Appert,J.Stat.Phys.94,1(1999).[7]J.Krug and H.Spohn,in Solids Far from Equilibrium ,edited by C.Godr´e che (Cambridge University Press,Cambridge,1991),p.412.[8]B.Derrida and K.Mallick,J.Phys.A 30,1031(1997).[9]S.-C.Park,J.-M.Park,and D.Kim,unpublished.[10]E.Brunet and B.Derrida,Phys.Rev.E 61,6789(2000).[11]D.Kim,Phys.Rev.E 52,3512(1995).[12]M.Henkel and G.Sch¨u tz,Physica A 206,187(1994).[13]T.C.Choy and F.D.M.Haldane,Phys.Lett.90A ,83(1982).[14]E.H.Lieb and W.Liniger,Phys.Rev.130,1605(1963).[15]J.G.Muga and R.F.Snider,Phys.Rev.A 57,3317(1998).[16]W.Krauth,Phys.Rev.B 44,9772(1991).(a)ω-0.10.1-0.50.5(b)Re k Im k 0FIG.1.For the first excited state,(a)the quantum num-bers I j ’s are depicted in the complex-ωplane with ω=e 2πiI/L and (b)the quasi-particle momenta k j ’s are shown in the complex-k plane.Here,the size of the system L is 20,the number of particles n is 10,and the attractive interaction U is 0.0025.The filled circle in (a)is where the two quantum numbers overlap.0.5 1102030EL n =2 U =0.05ground state first excited state0.5 1102030EL n =2 U =0.5ground state first excited state-3.4-3.3-3.2 102030EL n =2 U =5ground state first excited state0.5 11020 30EL n =3 U =0.05ground state first excited state-0.5 0 0.5 1020 30ELn =3 U =0.5ground state first excited state-12.17-12.16-12.15 1020 30ELn =3 U =5ground state first excited stateFIG.2.Ground-state energies and first excited-state ener-gies are plotted versus the size of the system L (4≤L ≤30)for U =0.05,0.5,and 5in the two-and the three-particle sectors.The dotted line represents E =0.For all values of U and L ,the ground-state energy is negative.On the other hand,when U =0.5,the excited-state energy becomes nega-tive near L ≃14in the two-particle sector and L ≃6in the three-particle sector.The signs of the excited-state energies for U =0.05and 5do not change in the range of L shown here.0.0010.010.1110102030∆LU=0.05U=0.5U=5FIG.3.Log-log plot of the excitation gaps (∆)versus the size of the system (L )in the two-particle sector.Data for U =0.05and 5approach straight lines with slope z =2.0,but those for U =0.5show a strong crossover before approach-ing the asymptotic behavior.The solid line for U =0.5is that fitted in the range 14≤L ≤18,and shows an effective z ≃2.4.0.00010.001 0.010.1110102030∆LU=0.05U=0.5U=5FIG.4.Same as in Fig.3,but for the three-particle sec-tor.The fitted solid line used the data for 8≤L ≤12,and has a slope of approximately 2.7.(a)k (b)k FIG.5.Distributions of the quasi-particle momenta,k j ’s,for the ground state (filled circles)and the first excited state (open circles)are shown in the complex-k plane for n =2.The size of the system L is 100and the interaction U is (a)0.001and (b)0.1.22.22.4s U510z e f fU L/πFIG.6.Effective exponent z effin the two-particle sector versus the scaling variable UL/πat L =10000.The interac-tion U varies from 0.0001to 0.001.At UL/π=s U ≃2.181,z eff≃2.401.。

摘要摘要天线作为MIMO系统中不可或缺的组成部分，其性能的好坏决定了该系统品质的优劣。

随着系统朝着小型化、集成化的方向发展，在尺寸受限的空间中放置多根天线，使得天线单元间的间距减小，不可避免的造成低隔离度，高相关性。

本文的研究主要针对提高双频MIMO天线的隔离度，通过在天线的馈电端口添加解耦网络的方法实现解耦。

该方法中移相、解耦、匹配的设计依次进行，设计思路清晰，天线的设计和解耦网络的设计分开进行使其具有一定的普遍性。

本文的主要研究工作包括：首先，在天线单元中以并联的形式添加解耦网络，通过将散射矩阵变换成导纳矩阵的方法，分析得出用导纳形式所表示的双频解耦条件和匹配条件。

为了增强天线的匹配性能，分析得出LC集总元件的匹配网络和阶梯阻抗的匹配网络。

其次，采用中和线解耦，根据耦合天线的解耦条件，获得中和线的解耦特性参数，讨论分析了阶梯阻抗线和均匀阻抗线作为移相网络对天线匹配性能的影响，以及LC集总元件匹配网络在增强天线阻抗匹配中的拓扑结构，经过仿真和加工实物，天线的隔离度在低频段提高了15dB以上，高频段提高了9dB以上。

接着，根据耦合谐振的方法分析得出由耦合参数组成的导纳矩阵，根据双频解耦条件和匹配条件，基于阶梯阻抗线设计了由开口谐振环组成的双谐振器作为解耦网络。

由阶梯阻抗线构成的匹配网络来补偿移相网络对天线原有匹配的破坏，增强其匹配性能。

最后用环形谐振器替换掉双谐振器作为解耦网络，运用奇耦模的分析方法得出环形谐振器的互导纳参数，令其满足解耦条件获得环形谐振器的初值，通过采用优化的方法得到高隔离度的天线单元。

带有两种不同解耦网络的天线隔离度无论是在低频还是在高频都提高到20dB以上。

关键词：MIMO，隔离度，导纳，解耦网络，匹配网络ABSTRACTThe antenna is an indispensable part of the MIMO system,the performance of the antenna determines the quality of the system.As the system grows in the direction of miniaturization and integration,multiple antennas are placed in the space of limited size, resulting in a reduction in the spacing between the antenna elements,which inevitably results in low isolation and high correlation.The research of this paper mainly aims at improving the isolation of dual-band MIMO antenna,and decoupling by adding decoupling network to the feed port of the antenna.The design of the phase shift, decoupling and matching of the method is carried out in turn,the design idea is clear, the design of the antenna and the design of the decoupling network are carried out separately to make it have a certain universality.The main research work of this paper includes:Firstly of all,the decoupling network is added in parallel in the antenna unit,and the method of transforming the scattering matrix into admittance matrix is used to analyze the dual-band decoupling condition and matching condition expressed by admittance.In order to enhance the matching performance of the antenna,the matching network of the LC lumped element and the matching network of the step impedance are analyzed.Secondly,the decoupling characteristic of the neutralization line is obtained according to the decoupling condition of the coupled antenna.The influence of the step impedance line and the uniform impedance line as the phase shift network on the antenna matching performance is analyzed and discussed.The LC lumped element matching networks in the enhanced antenna impedance matching with different ttopologies are also analyzed and discussed.After simulating and processing of physical，the antenna isolation is improved by more than15dB at low frequencies and 9dB at high frequencies.Thirdy,according to the coupled resonant method,the admittance matrix composed of coupling parameters is obtained.Based on the double-frequency decoupling condition and matching condition,a double resonator composed of an open resonant ring is designed as a decoupling network based on the step impedance line.The matching network composed of the step impedance line compensates the damage of the phase shift network to the original matching of the antenna and enhances its matchingperformance.Finally,the double resonator is replaced by the ring resonator as the decoupling network.The odd-even model method is used to obtain the admittance parameter of the ring resonator,which satisfies the decoupling condition to obtain the initial value of the ring resonator.The antenna unit with high isolation is obtained by the method of optimization.Antenna isolation with two different decoupling networks is increased to more than20dB at both low frequency and high frequency. Keywords:MIMO，The isolation，Admittance，Decoupling network，Matching network目录第一章绪论 (1)1.1课题研究的背景与意义 (1)1.2国内外研究现状 (2)1.3本文的组织安排 (6)第二章天线基础知识概述 (8)2.1MIMO技术概述 (8)2.1.1MIMO技术原理 (8)2.1.2MIMO技术特点 (9)2.2天线技术概述 (10)2.2.1天线的主要功能 (10)2.2.2天线的辐射原理 (10)2.2.3天线的特性参数 (12)2.3MIMO天线设计要求 (15)2.4本章小结 (15)第三章天线的耦合以及解耦分析 (16)3.1天线间的互耦以及互耦对天线的影响分析 (16)3.1.1天线间的互耦分析 (16)3.1.2互耦对天线的影响分析 (17)3.2天线互耦分析方法 (18)3.3天线解耦原理 (20)3.3.1解耦网络基本模型 (21)3.3.2双单元天线的解耦分析 (22)3.3.2.1双单元天线的单频解耦分析 (23)3.3.2.2双单元天线的双频解耦分析 (26)3.4本章小结 (31)第四章中和线解耦 (32)4.1中和线在提高天线隔离度中的应用 (32)4.1.1双频对称天线的设计 (32)4.1.2双频移相网络的分析 (33)4.1.3中和线解耦原理推导 (34)4.1.4匹配网络的设计 (36)4.2中和线解耦的天线加工测试 (40)4.2.1中和线解耦原理分析 (40)4.2.2天线性能测试 (42)4.3本章小结 (45)第五章谐振器解耦 (46)5.1双谐振器解耦原理分析 (46)5.2双谐振器在提高天线隔离度中的应用 (50)5.2.1双频对称天线的设计 (50)5.2.2双频移相网络的分析 (51)5.2.3开口谐振环组成的解耦网络分析 (53)5.2.4匹配网络分析 (56)5.3双谐振器在提高天线隔离度中的应用 (58)5.3.1双谐振器解耦原理分析 (59)5.3.2天线性能测试 (60)5.4环形谐振器在提高天线隔离度中的应用 (62)5.5带有环形谐振器的天线加工测试 (66)5.5.1环形谐振器解耦原理分析 (67)5.5.2天线性能测试 (68)5.6本章小结 (70)第六章全文总结与展望 (71)致谢 (73)参考文献 (74)攻读硕士学位期间取得的成果 (79)第一章绪论第一章绪论1.1课题研究的背景与意义无线通讯是使用非常广泛，也是瞬息万变，发展速度非常迅猛的科学技术，它促进经济进步和给人们的日常交流带来了完全不受时间、地点限制的便捷。

保罗·利科（Paul Ricoeur）保罗·利科（1913-2005），法国著名哲学家、当代最重要的解释学家。

他出生于法国南部城市瓦朗斯，先后就读于雷恩大学和索邦大学（巴黎四大），曾就读于斯特拉斯堡大学、索邦大学、南泰尔大学（巴黎十大）和鲁汶大学，病曾担任芝加哥大学、耶鲁大学、蒙特利尔大学的客座教授。

利科视野开阔，涉猎广泛。

他会通大陆哲学与英美哲学、存在主义与结构主义、解释学与批评理论、弗洛伊德的心理分析与黑格尔的辩证法、文学理论与宗教哲学等，被誉为哲学领域久负盛名的翻译家。

利科著作等身，曾出版学术著作逾20部，范围涉及现象学、解释学、语言学、心理学、马克思主义、宗教学和政治学等。

他曾翻译胡塞尔等人的哲学著作，并进行过深入的翻译理论思考。

晚年出版的《翻译论》（sur la traduction,2004）一书，是其翻译思想的集中体现。

本文便选自该书英文版。

在文中，利科提出翻译的两种范式：一是语言学范式，即从狭义上讲，翻译是语言间的话语信息的转变；二是本体论范式，即从广义上讲，翻译是同一话语社区内对整体意义的阐释。

这两大途径都是合理合法的，第一种途径以贝尔曼为代表，认为翻译是“异域的考验”；第二种途径以斯坦纳为代表，认为“理解即翻译”。

利科认为，一方面由于人类语言的多样性和独特性，翻译是有必要的，但在理论和先验上似乎又是不可能的。

但是，从另一个方面来看，人类几千年以来一直在从事“不可能”的翻译活动，这又是不争的事实。

因此，传统的“可译性”与“不可译性”模式没有意义。

取而代之的，应该是一种更具实践色彩的“忠实”与“背叛”新模式。

利科的哲学翻译思想充满了对话和辩证性，既接受各大流派思想的影响，又具有敏锐的批判精神。

他指出，翻译是个理论上困难、实践上相对简单的问题。

如果翻译在实践层面是可能的，那么在语言多样性的背后必定隐藏着某些结构。

这些结构要么携有已经失去，但必须找回的原初语言的痕迹，如本雅明所谓的“纯语言”；要么由一些先验的符码或普通结构组成，我们必须对其进行重建，如艾特等人所谓的“完美语言”。

高级氧化技术数据优异的开发与应用水务工程一班乔丹09290120110关键词: 高级氧化；EE/O；EE/M；电能注：此立场文件正在考虑通过，由IUPAC光化学委员会通过高级氧化技术处理受污染的水域的建议采取措施，我征求意见，并应为第一作者。

高级氧化工艺（AOPs），涉及在原位生成高度烈性化学氧化剂如液压（•OH），最近出现一类重要的技术，用于加速破坏各种各样污染的水和空气中的污染物。

我建议采取普遍适用的标准数字来比较这些废物处理技术。

这些数据显示的优点是基于电能消耗在两个现象级动力学制度：一为浓度（每单位质量的电能，EE/M）和一个低浓度（每立方米每个数量级的电能，EE/O级）。

我们还指出，一个简单的整体动力学可以理解为有机物破坏废物流的行为（即，无论是零或一阶），是描述电能的效率所必要的。

这些标准的数字的优点是提供了直接链接到电效率（值越低意味着更高的效率）的一种高级氧化过程，独立的系统性质，因此允许直接比较各种不同的AOP技术。

我们还表明，EE/O和EE/M参数是成反比的基本效率因子，如灯的效率，所发射的光束的馏分被水和生成的量子产率活性自由基所吸收。

介绍高级氧化工艺（AOPs），其中涉及中原位生成高度有效的化学氧化剂，如羟基基团•OH），最近出现了（1）作为一类重要的加速氧化的技术，从而破坏了受污染的水和空气中的各种各样的有机污染物，这些过程中的部分列表包括：均质紫外线照射（2）（无论是直接照射的污染物或光解氧化介导的过氧化氢（UV/H2O2）和臭氧(UV/O3)多相光催化）（3）使用半导体催化剂（UV/TiO2，），电子束照射（4），X-射线或γ-射线辐解，非热性的放电（5）超临界水（6）超声波照射（超声波）（7）电气蚀。

这些技术涉及广泛，以及作为氧化剂生成的不同的激活方法，并且能够有可能利用一些不同的机制破坏有机物。

然而所有的这些过程，是电驱动和共享的羟基自由基化学的共同点（至少部分地）。

GeothermalEnergy(TPO21-1)Earth’s internal heat, fueled byradioactivity, provides the energy for plate tectonics, continental drift,mountain building, and earthquakes. It can also be harnessed to drive electricgenerators and heat homes. Geothermal energy becomes available in a practica form whenunderground heat is transferred by water that is heated as it passes through asubsurface region of hot rocks (a heat reservoir) that may be hundreds orthousands of feet deep. █The water is usually naturallyoccurring groundwater that seeps down along fractures in the rock; lesstypically, the water is artificially introduced by being pumped down from thesurface. █The water is brought to thesurface, as a liquid or steam, through holes drilled for the purpose. █By far the most abundant form ofgeothermal energy occurs at the relatively low temperatures of 80℃ to 180℃ centigrade. █Water circulated through heatreservoirs in this temperature range is able to extract enough heat to warmresidential, commercial, and industrial spaces. More than 20,000 apartments inFrance are now heated by warm underground water drawn from a heat reservoir ina geologic structure near Paris called the Paris Basin. Iceland sits on avolcanic structure known as the Mid-Atlantic Ridge. Reykjavik, the capital ofIceland, is entirely heated by geothermal energy derived from volcanic heat.Geothermal reservoirs with temperaturesabove 180℃ centigrade are useful for generatingelectricity. They occur primarily in regions of recent volcanic activity ashot, dry rock; natural hot water; or natural steam. The latter two sources arelimited to those few areas where surface water seeps down through undergroundfaults or fractures to reach deep rocks heated née the recent activity ofmolten rock material. The world’s largest supply of natural steam occurs at TheGeysers, 120 kilometers north of San Francisco, California. In the 1990s enoughelectricity to meet about half the needs of San Francisco was being generatedthere. This facility was then in its third decade of production and wasbeginning to show signs of decline, perhaps because of over development. By thelate 1990s some 70 geothermal electric-generating plants were in operation in California,Utah, Nevada, and Hawaii, generating enough power to supply about a millionpeople. Eighteen countries now generate electricity using geothermal heat.Extracting heat from very hot, dryrocks present a more difficult problem: the rocks must be fractured to permitthe circulation of water, and the water must be provided arterially. The rocksare fractured by water pumped down at very high pressures. Experiments areunder way to develop technologies for exploiting this resource.Like most other energy sources,geothermal energy presents some environmental problems. The surface of theground can sink if hot groundwater is withdrawn without being replaced. Inaddition, water heated geothermal can contain salts and toxic materialsdissolved from the hot rock. These waters present a disposal problem if theyare not returned to the ground from which they were removed.The contribution of geothermal energyto the world’s energy future is difficult to estimate. Geothermal energy is in a sensenot renewable, because in most cases the heat would be drawn out of a reservoirmuch more rapidly than it would be replaced by the very slow geologicalprocesses by which heat flows through solid rock into a heat reservoir.However, in many places (for example, California, Hawaii, the Philippines,Japan, Mexico, the riftvalleys of Africa) the resource is potentially so largethat its future will depend on the economics of production. At present, we canmake efficient use of only naturally occurring hot water or steam deposits.Although the potential is enormous, it is likely that in the near futuregeothermal energy can make important local contributions only where theresource is close to the user and the economics are favorable, as they are inCalifornia, New Zealand, and Iceland. Geothermal energy probably will not makelarge-scale contributions to the world energy budget until well into thetwenty-first century, if ever.1. According to the processes describedin paragraph 1, what is the relationship between radioactivity and the steamproduced by geothermal heat?Geothermally heated steam is producedwhen water is exposed to radioactivity deep underground.When water is introduced into holesdrilled thousands of feet in the ground, it becomes radioactive and turns tosteam.Radioactivity heats Earth's interiorrock, which in turn can heat water to the point it becomes steam.When a reservoir of steam in subsurfacerock is produced by radioactivity, it is said to be geothermally heated.2. The word "practical" in the passage is closest in meaning tousableplentifuleconomicalfamiliar3. The word "abundant" in the passage is closest in meaning toeconomicalfamiliarplentifuluseful4. According to paragraph 2, which of the following is true about heat reservoirs with a temperature in the range of 80° to 180° centigrade?They are under international control.They are more common than reservoirs that have a higher temperature.Few of them produce enough heat to warm large industrial spaces.They are used to generate electricity.5. According to paragraph 3, what is the connection between underground faults and naturally occurring steam?Underground faults enable the heat from molten-rock material to escape upward to regions where it can heat surface water enough to produce steam.Underground faults are created by steam that is produced in geothermal reservoirs deep inside Earth.Underground faults create spaces in which natural steam is sometimes trapped. Underground faults allow surface water to reach deep rocks that are hot enough to turn it into steam.6. In paragraph 3, why does the author mention that in the 1990s The Geysers was in its third decade of production?To provide the historical context of the geothermal production of electricity in the United StatesTo imply that The Geysers was the first geothermal site to be put into production in CaliforniaTo help explain the signs of decline shown by The GeysersTo explain why 70 new geothermal sites were put into electricity production in the late 1990s7. Which of the following can be inferred from paragraphs 2 and 3 about geothermal reservoirs?Volcanic heat is associated only with geothermal reservoirs that have a temperature over 180° centigrade.More countries produce power from geothermal reservoirs than use them for heating buildings.Most geothermal reservoirs are suitable for producing electricity.A higher geothermal reservoir temperature is needed to generate electricity than is needed to heat homes.8. According to paragraph 4, extracting heat from very hot, dry rocks is difficult in part becausethe underground rock must be fractured before heat can be removed from itthe water above the rock is under very high pressurethe rock breaks apart when water is pumped into itthe water circulated through the rock must be much cooler than the rock itself9. The word "exploiting" in the passage is closest in meaning tolocatingincreasingmaking use ofestimating the size of10. How is the problem that the surface may sink related to the problem that water heated geothermally may contain toxic materials?Both problems could be solved by returning groundwater that is removed from an underground heat reservoir back to the reservoir after heat is extracted from it.The problem of sinking is more difficult to solve than is the problem of toxic materials. Land at the surface sinks because the rock beneath the surface is weakened when salts and toxic materials are removed from it in the process of extracting geothermal energy.Both problems are caused by the fact that the hot groundwater in a heat reservoir dissolves the rock, which weakens the rock and makes the water toxic with salt.11. Which of the sentences below best expresses the essential information in the highlighted sentence in the passage? Incorrect choices change the meaning in important ways or leave out essential information.Heat flows through solid rock very slowly, so it takes a very long time for geological processes to produce a reservoir of geothermal energy.Geothermal energy is not renewable because heat flows very slowly through solid rock into or out of a heat reservoir.The heat quickly removed from a heat reservoir is replaced so slowly by geological processes that geothermal energy is not practically speaking, renewable.In most cases, heat travels into a heat reservoir so slowfy that it is a much quicker process to remove the heat from a reservoir than to replace it.12. In paragraph 6, the author implies that in California, Hawaii, the Philippines, Japan, Mexico, and the rift valleys of Africa the potential size of the geothermal resource is so large thatit might be economically worth developing these sites even though geothermal energy is not renewablethese sites will be the first geothermal energy sites to be developed witb new technology these sites are likely to make a large-scale contribution to the world energy budget in the twenty-first centuryit does not matter whether they have naturally occurring deposits of hot water or steam13．Look at the foursquares [█] that indicate where the followingsentence could be added to the passage. <i> In either case,the heated water will usually be under considerable pressure, and so may have atemperature that is well above its sea-level boiling point of 100°centigrade.</i>Where would the sentence best fit? Click on asquare to add the sentence to the passage.████14．Directions: An introductory sentence for a brief summary ofthe passage is provided below. Complete the summary by selecting the THERRanswer choices that express the most important ideas in the passage.Somesentences do not belong in the summary because they express ideas that are notpresented in the passage or are minor ideas in the passage. This question is worth 2 points.Heat reservoirs in the form of hot rock farbeneath Earth's surface are a potential source of usable geothermal energy.·Heat reservoirs with a temperature from 80° to 180° centigrade can be used, as in France and Iceland, to heat buildings.·A number of countries now use geothermal reservoirs that contain water or steam above180° centigrade to generate electricity.·Most heat reservoirs with a temperature above 180° centigrade cannot be used for energy because they are usually too close to recent volcanic activity.·The sinking of land above heat reservoirs and other environmental problems arise when water is pumped into a heat reservoir under high pressure.·Experiments are under way to determine if geothermally heated waters could be used as a source of certain minerals that have been dissolved out of hot rocks deep within Earth. ·A number of issues, including how to extract heat from reservoirs that do not have a natural supply of water, will significantly limit the use of geothermal energy for the foreseeable future.答案解析：1. 细节题，问radioactivity和steam的关系，所以找双关键词，分别定位至本段第一句和最后一句，第一句说radioactivity提供了地球的内热，最后一句说水变成蒸汽到达地表，水受热才能蒸汽，而这份热量是geothermal energy提供的，这就是二者的关系，所以答案是C。

a r X i v :n u c l -t h /9901065v 1 22 J a n 1999Testing Low Energy Theorems in Nucleon-Nucleon ScatteringThomas D.CohenDepartment of Physics,University of Maryland,College Park,MD 20742-4111James M.HansenMontgomery Blair High School,Silver Spring,MD 20901Low energy theorems have been derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading nontrivial order in an expansion based Q counting,a scheme in which both m πand 1/a (where a is the scattering length)are treated as small mass scales.Previous tests of these theorems based on coefficients extracted from scattering data indicate a pattern of gross violations which suggested serious problems for the perturbative treatment of pions implicit in Q counting.We discuss the possibility that uncertainties associated with extracting the coefficients from the scattering data make such tests invalid.Here we show that errors in the s-wave phase shift extractions are sufficiently small to test direct test predictions from Q counting at next to leading order.In particular we show that there exist low energy theorems for the sum of all terms in the effective range expansion beyond the first two which allow for precise tests.These low energy theorems fail badly which suggests that pionic aspects of Q counting are not under control.I.INTRODUCTIONThere has been considerable interest in the use of effective field theory (EFT)techniques in nuclear physics during the past several years [1–30].Much of the goal of this work is to use power counting ideas associated with chiral symmetry to nuclear physics.This is not simple since apart from m π,the inverse s-wave scattering length,1/a is another light scale in the problem.Many of the approaches beginning with Weinberg’s [1]formulate the expansion at the level of a two-particle irreducible kernel rather than for observables.While such an approach provides an organizing principle for calculations,it provides no systematic estimate of the accuracy of particular observables in terms of power counting.Recently a scheme was introduced in which observables can be expressed in terms of a consistent power counting scheme [21,26–29].This scheme is based on power counting in a single scale,Qm π∼Q 1/a ∼Q k ∼Q (1)In this power counting,all other scales are assumed to be heavy and will collectively be symbolized by Λ.This power counting scheme describes low momentum physics in that k/Λ≪1.There can be rapid momentum dependence of some observables,however,since the expansion for any observable includes all orders in ka and k/mπ.This power counting scheme has been implemented using dimensional regularization [21,28,29]and directly in configuration space using a cutoff[26].We note in passing the fact that1/a is formally treated as being of the same order as mπand k is not emphasized in the original papers of Kaplan, Savage and Wise[21,22].It is implicit,however,in the expression for the leading order(Q−1)amplitude which is given by−4π/[M(1/a+ik)].Note that if k and1/a were of different orders one could expand out the denominators.One test that the Q counting formally involves treating1/a as being of the same order is found in the cutofftreatment of ref.[26]where the rules in eq.(1)were explicitly used to derive an expression for the phase shifts which is formally equivalent to the expressions derived by Kaplan,Savage and Wise[21,22].In a previous paper[27]we used Q counting to derive low energy theorems for coefficients of the effective range expansion(ERE)at leading nontrivial order in Q counting.The ERE is a parameterization of s-wave scattering given byk cot(δ)=−12r e k2+v2k4+v3k6+v4k8+ (2)and is particularly useful in the case of unnaturally large a.The v i coefficients at this order arefixed entirely by mπand1/a.The low energy theorems were compared with v i extracted from a partial wave analysis of the scattering data.All of the predictions were many times larger than the v i extracted from scattering data.As the low energy theorems are particularly sensitive to pion physics(all terms are nonanalytic in mπ) a plausible conclusion from this discrepancy is that the part of Q counting associated with the expansion of mπ/Λhas broken down.Such a conclusion is consistent with the many successes of Q counting[22] for deuteron properties provided such successes depend essentially on the expansion of1/(aΛ)rather than mπ/Λ.Indeed,in ref.[22]the authors show that the the effective range expansion without explicit pions does a better job of describing the form factors at low momentum transfers than the theory based on Q counting with explicit pions.This is precisely what one would expect if the1/(aΛ)expansion were working and the mπ/Λfailing.The scenario whereΛis numerically of the same scale as mπis quite plausible.The essence of Q counting is that the only long distance scales are a and1/mπ.As a practical matter one should identify1/Λas the longest of the various short distance scales in the problem as that will be the scale responsible for a breakdown of the expansion.The effective range,r e,is an important scale characterizing low energy nucleon-nucleon scattering.Numerically it is∼2.7fm in the singlet channel and∼1.7fm in the triplet channel.In both cases,r e mπ>1.If one identifies1/r e as a short distance scale,Λ,then mπ/Λ>1and a chiral expansion is not valid.Two issues must be resolved before coming to such a conclusion.Thefirst is whether r e is a“short distance”scale(which just happens to be numerically long),and the second is whether the appropriate scaleis1/r e,or1/r e times some numerical factor which if large enough might render the chiral expansion useful. Thefirst issue can be easily resolved in the context of Q counting.If in Q counting,r e were of order Q−1,for example,scaling as a or1/mπ,then the large numerical value of r e would be natural.However, the effective range has been calculated at leading nontrivial order in Q counting(i.e.,next to leading order) [29]and it is explicitly seen that r e∼Q0.Thus,the value of r e in the context of Q counting is determinedby short distance scales.This in turn suggests that the longest scale treated as short distance in Q counting (namely r e)is comparable to or larger than the shortest longest scale(1/mπ).The fact that r e mπ≥1 suggests that the chiral expansion may not be under control even when the unnaturally large scattering length is taken into account.The issue of whether the large value of the effective range invalidates the chiral aspects of Q counting is central to the effectivefield theory program in nuclear physics.The question of whether the low energy theorems of ref.([27])are badly violated is,in turn,a critical issue in assessing the viability of the chiral aspects of the Q counting scheme.Recently,Mehen and Stewart[28]have raised the question of whether errors in the phase shifts render a reliable extraction of the v i coefficients impossible.They make a crude estimate of the errors of the v2in the triplet channel coefficient including the uncertainties using the reported values from the Nijmegen partial wave analysis for k<70MeV along with the scattering length and effective range and obtain v2=−.50±.52±∼.1fm3,where thefirst error is a quadrature sum of the estimates errors and the second uncertainty is a theoretical estimate of the contributions from the v3and higher terms.This estimate is consistent with both the valuefit from the Nijmegen analysis[32],vfit2=.04fm3,and the low=ing the second lowest report point from the Nijmegen energy theorem prediction value of v LET2analysis they estimate the v2=.03±.04±∼.5fm3.Accordingly they conclude that there is too much uncertainty in the extraction of the v i coefficients to make a sharp test of the low energy theorems.In this paper we will show that data are sufficiently good so that sharp tests of the low energy theorems of ref.[27]are possible and that the theorems are,in fact,badly violated.The most sensitive method is to consider weighted sums of the low energy theorems of the v i coefficients which can be extracted with far greater than precision than the individual terms.In particular,we test the total contribution to k cotδarising from all of the higher terms(v2and above)in the effective range expansion.In this paper we will√focus on tests in the triplet channel.One particularly nice place to test is at the deuteron pole(k=idenote it,S(k2).Thus,S(k2)≡k cot(δ)−−12r e k2 (3)= j≥2v j k2j(4) where the second equality holds only within the radius of convergence of the effective range expansion.Note, however,that the general definition holds for all k2.The shape function,S(k2),can be calculated in the Q ing the expression for k cot(δ)in ref.[27]which can be obtained using either a cutoffscheme or dimensional regularization with either PDS or OS subtraction,onefinds at order Q2for either the singlet or triplet channelS LET(k2)=g2A M a2−2mπ3mπa−2a2g2A Mk2 ln1+4k2a g2A Mk tan−12k64πf2πln 1+4k2(j−2)!∂2S LET16πf2π −165a m3π−216πf2π 167a m5π+1616πf2π −2569a m7π−16Note that the prediction of the shape function S(k2)depends on no free parameters and thus is a low energy theorem in the same sense that the predictions for the v i’s are low energy theorems.The low energy theorem for S(k)is more basic than the low energy theorems for the v i;all the predicted v i follow from eq.(5). It is also important to note that S(k2)atfixed k2is far easier to extract from the data with reliable error estimates than v i since all that is needed to be known is the phase shift,the scattering length and effective range,along with knowledge of their errors.One does not need to know enough information to accurately deduce higher derivatives of the function.It should be noted,that within the radius of convergence of the effective range expansion,i.e.for k2<m2π/4,testing the predicted S(k2)tests a sum of the low energy theorems for the v j weighted by k2j.However,as noted above there is no necessity to restrict tests of S(k2) to this regime.It is important to note that the shape function,S(k2),like the individual v j’s provide an ideal way to probe the pionic aspects of the Q counting scheme.Recall that in the Q counting scheme there are two small mass scales apart from the external momentum,1/a and mπ.However,1/a<<mπ.Thus,it remains possible that the underlying“short distance”scale,Λ,is in fact comparable to mπwhile1/a<<Λ.If such a situation occurs one expects observables primarily sensitive to1/(aΛ)to be well described, whereas observables primarily sensitive to mπ/Λto be poorly described.We note that this possibility is not implausible given experience with potential models which arefit to the data where it is generally seen that the non-one-pion-exchange part of the potential remains significant at ranges comparable to1/mπso that there is a“short distance”scale in the problem of the pionic range[26].The most straightforward way to test whether the mπ/Λexpansion is under control is to compare predictions from a theory with pions integrated out to those which include pions and see whether one gets systematic improvement by including the pions.Unfortunately for generic observables this test is not very clean since the observable may be completely dominated by the1/(aΛ)expansion.On the other hand,if one has an observable which vanishes at some order in the pion-integrated out theory but not in the pion-included theory than one has a prediction which explicitly tests the pionic contributions.The shape function,S(k2),at order Q2is such an example (as are the v i coefficients derived from it).The reason for this is that k cotδin the pion-integrated-out theory is just the effective range expansion,which at order Q2truncates at the second term and implies that S(k2)=0at this order.Thus the predictions of S(k2)provides a sharp test of the pionic part of Q counting.In this paper we will restrict our attention to the triplet channel as in that channel a and r e have been extracted from the partial wave analysis with very small error bars[34]allowing for a very sharp test.They are given bya=5.420±.001fm r e=1.753±.002fm(8) An additional advantage to working in the triplet channel is the existence of the deuteron bound state which corresponds to a pole in the scattering amplitude when it is analytically continued to imaginary momentum.Define the quantity,γ,asγ=√a +1whether,as suggested in ref.[28],the uncertainties are too large.The difficulty of accurately extracting high derivatives of functions from data with uncertainties is clear.Fortunately,there are effectively several distinctfits to the scattering data.Note that the Nijmegen group not onlyfit the data directly in their partial wave analysis[32],they alsofit several potential models directly to the data—i.e.,not the the partial wave analysis phase shifts with aχ2per degree of freedom of1.03, essentially unity[33].In effect,as noted in ref.[33],the phase shifts produced by these potential models represent parameterizations of the partial wave analysis phase shifts.Now,as discussed in ref.[34]the effective range expansion coefficients v j extracted from the various potential models agree with each other and with the v i extracted directly from the bestfit values of the partial wave analysis to an extremely high precision.This is quite useful,since the bias introduced is presumably quite different in the the variousfits. Thus,overall the spread between the various potential models and the directfit to the partial wave analysis should provide some sense of the scale of the uncertainty.In table II we reproduce the triplet channel v j extracted from the partial wave analysisfits and from the potential models and the values from the low energy theorems.Note that for all cases the spread between the different extracted values is quite small.The largest relative spread is in the v2coefficient values and that is presumably because v2is accidentally very small.In all cases,the spread in the values of the coefficients is vastly smaller than the difference from any of these values to the one predicted by the low energy theorems. This strongly suggests that the individual v j coefficients are known well enough to test the low energy theorems and that low energy theorems make predictions inconsistent with the data.III.DISCUSSIONBy focusing on the quantity S(k2),we have been able to show that at least one pion aspect of Q counting fails badly at next to leading order.¿From our analysis it is clear that if the uncertainty estimates of ref.[32] are even approximately correct,then the predictions for S(k2)from the low energy theorems are in marked disagreement with the data,even to the point of getting the sign wrong.One obvious explanation for this is the one advanced in our previous paper[27]and discussed in the introduction,namely that1/mπis not long ranged compared to other scales in the problem.This possibility is plausible on its face,since it is known in nuclear physics that there are many length scales which are comparable to1/mπbut which have no obvious chiral origin.The effective range is a good example.Another example is the characteristic ranges of the non-pion-exchange part of nuclear potential which arefit to phase shifts(although as discussed in ref.[8] the need tofit the effective range constrained the non-pionic part of the potential to be long).While this does not prove that the pionic part of Q counting must fail,it certainly makes it very plausible.If the failure of the low energy theorems for scattering indicates a systematic failure of pionic effects of s-wave properties in Q counting,one expects failure for other observables in the sense that the explicit inclusion of pions should not lead to improved predictive power.The recent calculations of deuteron formfactors in ref.[22]strongly support this view.The calculation of the form factors using a simple effective range expansion treatment including up to the effective range describes the data better than the next-to-leading order treatment including explicit pions.Had the pionic aspects of Q counting been under control one would have expected the calculation including explicit pions would have improved things.At present we know of no observable associated with s-wave two nucleon states for which the inclusion of explicit pions in Q counting improves predictions and several for which it worsens them.Of course,this does not prove that the mπ/Λexpansion will generally fail for all s-wave observables.It remains possible, for example,that one coefficient in the next-to-leading order theory is accidentally large and that byfitting it and working at next-to-next-to leading order the usefulness of the mπ/Λwill be manifest.The authors of ref.[22]assert(without proof)that at higher orders the effectivefield theory with pions will work better than the simple effective range calculation since it has the correct underlying physics.We believe that this scenrio is unikely in view of the fact that there seems to be no scale separation between1/mπand“short distance”scales.It is clear how to test this idea:calculate observables at higher order for theories with and without explicit pions and compare the qualities of the prediction.In doing such comparisons,however,it is essential to distinguish the quality of the descriptions of the underlying physics from the quality of mere curvefitting. Accordingly,in such comparisons it is essential that the theories with the same number of parameters be compared and the same prescriptions forfitting.Thus,for example the appropriate test for the deuteron form factors of ref.[22]is not whether a higher order effectivefield theory calculation wit h pions out performs the simple effective range expansion—eventually it must,at least over some region,as one will have additional parameters to characterize the current operator.Rather,the test is whether the theroy with pions out performs an effe ctivefield theory with pions integrated out and with the same number of parameters. The authors thank Silas Beane and Daniel Phillips for interesting discussions.TDC gratefully acknowl-edges the support of the U.S.Department of Energy under grant no.DE-FG02-93ER-40762.[6]D.B.Kaplan,Nucl.Phys.B494,471(1997).[7]T.D.Cohen,Phys.Rev.C55,67(1997).D.R.Phillips and T.D.Cohen,Phys.Lett.B390,7(1997).S.R.Beane,T.D.Cohen and D.R.Phillips,Nucl.Phys.A632,445(1998),Ann.Phys.263(1998)255.[8]K.A.Scaldeferri,D.R.Phillips,C.W.Kao and T.D.Cohen,Phys.Rev.C56,679(1997).[9]J.L.Friar,Few Body Syst.99,1(1996),nucl-th/9607020.[10]M.J.Savage,Phys.Rev.C55,2185(1997),nucl-th/9611022.[11]M.Luke and A.V.Manohar,Phys.Rev.D55,4129(1997),hep-ph/9610534.[12]G.P.Lepage,nucl-th/9706029,Lectures given at9th Jorge Andre Swieca Summer School:Particles and Fields,Sao Paulo,Brazil,16-28Feb1997.[13]S.K.Adhikari and A.Ghosh,J.Phys.A30,6553(1997).[14]K.G.Richardson,M.C.Birse and J.A.McGovern,hep-ph/9708435;M.C.Birse,J.A.McGovern,and K.G.Richardson hep-ph/9807302.[15]P.F.Bedaque and U.van Kolck,PLB428,221(1998);P.F.Bedaque,H.-W.Hammer and U.van Kolck,PRC58,641(1998)[16]U.van Kolck,Talk given at Workshop on Chiral Dynamics:Theory and Experiment(ChPT97),Mainz,Germany,1-5Sep1997,hep-ph/9711222;nucl-th/9808007[17]T.S.Park,K.Kubodera,D.P.Min and M.Rho,hep-ph/9711463;T.S.Park hep-ph/9803417;T.S.Park,K.Kubodera,D.P.Min and M.Rho,nucl-th/9807054[18]J.Gegelia,nucl-th/9802038,nucl-th/9805008.[19]nucl-th/9806028.[20]J.V.Steele and R.J.Furnstahl,NPA637,1998(16).[21]D.B.Kaplan,M.J.Savage and M.B.Wise,Phys.Lett.B424,390(1998),nucl-th/9801034;nucl-th/9802075,to appear in Nucl.Phys.B;[22]D.B.Kaplan,M.J.Savage,and M.B.Wise,nucl-th/9804032,submitted to Phys.Rev.C[23]J-W.Chen,H.W.Griesshammer,M.J.Savage,and R.P.Springer nucl-th/9806080[24]T.D.Cohen in Proceedings of“Workshop on Nuclear Physics with Effective Field Theory”,to be published.[25]M.J.Savage,in Proceedings of“Workshop on Nuclear Physics with Effective Field Theory”,to be published,nucl-th/9804034.[26]T.D.Cohen and J.M.Hansen,nucl-th/9808006.[27]T.D.Cohen and J.M.Hansen,nucl-th/9808038.[28]T.Mehen and I.W.Stewart,nucl-th9809071.[29]T.Mehen and I.W.Stewart,9809095[30]J.V.Steele and R.J.Furnstahl,nucl-th/9808022.[31]Reviews of the effectivefield theory program generally can be found in:A.V.Manohar,hep-ph/9606222;andD.B.Kaplan nucl-th/9506035.[32]V.G.J.Stoks,R.A.M.Klomp,M.C.M.Rentmeester,and J.J.de Swart,PRC48,792(1993);on line athttp:nn-online.sci.kun.nl[33]V.G.J.Stoks,R.A.M.Klomp,C.P.F.Terheggen,and J.J.de Swart,PRC49,2950(1994)[34]J.J.de Swart,C.P.F.Terheggen,V.G.J.Stoks,nucl-th/9509032,invited talk at“Dubna Deuteron95”.lab energy(MeV)S low energy theorem(Mev) Deuteron Pole-0.743 1-0.02585-0.53510-1.7825-7.5450-20.10TABLE I.A comparison of the shape function,S(k2)=k cot(δ)+1/a−1/2r e k2for the3S1channel extracted from the Nijmegen partial wave analysis with the prediction by the low energy theorem of eq.(5)δ(3S1channel)v3(fm5)low energy theorem 4.6.040-3.96 Nijm I.675.045-3.95 Reid93.671。

Effect of a superheating and sub-cooling heat exchanger to the performance of a ground source heat pump systemKadir Bakirci *,Derya Colak 1Department of Mechanical Engineering,Atatürk University,25240Erzurum,Turkeya r t i c l e i n f oArticle history:Received 15November 2011Received in revised form 13April 2012Accepted 20April 2012Available online 7June 2012Keywords:Ground source heat pump Ground heat exchanger Cold climate HeatingSuperheating Sub-coolinga b s t r a c tThe aim of this study is to evaluate the effect of a superheating and sub-cooling heat exchanger (SHCHE)to the performance of ground source heat pump system for climatic condition of Erzurum having cold climate in Turkey.For this purpose,an experimental set-up was constructed.The experimental apparatus consists of a series ground heat exchanger (GHE),a liquid-to-liquid vapor compression heat pump,water circulating pumps and other measurement equipments.In this study,the performance of the systems with and without SHCHE was experimentally investigated.The experiments were performed in 2010for January and February which are the coldest months of the heating season.The experimentally obtained results were used to calculate the power values of the main system equipments,the coef ficient of performance of the heat pump (COP)and the overall system (COPS)for systems with and without SHCHE.Ó2012Elsevier Ltd.All rights reserved.1.IntroductionTurkey ’s demand for energy and electricity is increasing rapidly.Turkey is heavily dependent on expensive imported energy resources that place a big burden on the economy.As would be expected,the rapid expansion of energy production and consumption has brought with it a wide range of environmental issues at the local,regional,and global levels.With respect to global environmental issues,Turkey ’s carbon dioxide (CO 2)emissions have grown along with its energy consumption.States have played a leading role in protecting the environment by reducing emissions of greenhouse gases.In this regard,renewable energy resources appear to be one of the most ef ficient and effective solutions for clean and sustainable energy development in Turkey.Turkey ’s geographical location has several advantages for extensive use of most of these renewable energy sources [1].In future the world ’s energy supply must become more sustainable.This can be achieved both by a more ef ficient use of energy and by relying on renewable sources of energy,particularly wind,hydropower,solar and geothermal energy [2].Turkey is anenergy importing nation with more than half of our energy requirements met by imported fuels.Air pollution is becoming a signi ficant environmental concern in the country.Achieving solutions to environmental problems that we face today requires long-term potential actions for sustainable development.For the governments or societies to attain sustainable development,much effort has to be devoted to utilizing sustainable energy resources in terms of renewable energies [3,4].The GSHP (ground source heat pump)is one of the ef ficient and sustainable methods to provide space heating and hot water for various kinds of buildings.The GSHP,works by means of the vapor compression cycle,which cools a circulating fluid that flows through a system of closed loops.These loops are buried within the ground either horizontally,if land space permits,or vertically by means of boreholes.The direction of heat flow is from the ground to the cooler fluid and this heat is upgraded to a higher temperature through the vapor compression cycle for delivery to the building [5].The ground source heat pumps provide a new and clean way of heating buildings in the world.They make use of renewable energy stored in the ground,providing one of the most energy-ef ficient ways of heating.They are suitable for a wide variety of building types and are particularly appropriate for low environmental impact projects [6].In the literature,a number of investigations have been con-ducted by some researchers in the design,modeling and testing of the GSHP systems [7e 18].Healy and Ugursal [8]have investigated*Corresponding author.Fax:þ904422360957.E-mail address:abakirci@.tr (K.Bakirci).1Present address:Directory of the 12th Region of Highways,25080Erzurum,Turkey.Contents lists available at SciVerse ScienceDirectEnergyjournal ho me page:www.elsevier.co m/locate/energy0360-5442/$e see front matter Ó2012Elsevier Ltd.All rights reserved.doi:10.1016/j.energy.2012.04.049Energy 44(2012)996e 1004the effect of various system parameters on the GSHP performance using a computer model.They have also carried out a comparative economic evaluation to assess the feasibility of using a GSHP in place of conventional heating/cooling systems and an air source heat pump.Florides et al.[9]carried out a study on the geothermal characteristics of the ground and the potential of using ground coupled heat pumps in Cyprus.Yu et al.[11]designed a constant temperature and humidity system driven by a ground coupled heat pump and constructed in an archives building of Shanghai.The experimental results under weather condition in Shanghai were analyzed and,the investigation of the experiment in a year was presented.Pulat et al.[15]have investigated the performance of the horizontal closed-loop water-to-air ground source heat pump system including the effect of various parameters such as leaving temperature of ground heat exchanger unit and outdoor temper-ature for winter climatic condition of Bursa,Turkey.Blum et al.[16] determined and assessed the economic and technical factors that influence the design and performance of the GSHP systems in private households.Xi et al.[19]presented experimental studies on a solar-assisted ground coupled heat pump system for space heating.Four opera-tion modes of the system were investigated throughout the coldest period in winter.The heat pump performance,the borehole temperature distributions and the solar colleting characteristics of the system were analyzed.Jeon et al.[20]analyzed the performance of a hybrid cooling system that combines a screw water chiller with a ground source heat pump at various cooling loads.The SHCHE is used to superheat and sub-cool the refrigerant in outlet of the condenser and evaporator of the vapor compression heat pump system,respectively.The superheating and sub-cooling procedures are applied for improving the system efficiency.In the literature,available studies on sub-cooling and superheating effects of vapor compression refrigeration cycles are very limited.Selbas et al.[21]obtained optimum heat exchanger areas and optimum sub-cooling and superheating temperatures under various oper-ating conditions of vapor compression refrigeration system.The application was consisted of determining the optimum heat exchanger areas with the corresponding optimum sub-cooling and superheating temperatures.Various studies have been carried out by researchers in order to analyze the performance of the GSHP systems around the world. They performed theoretical and experimental studies on the ground source heat pump systems with a ground heat exchanger and concluded that using heat pump systems are feasible.This study includes the performance evaluation of the ground source heat pump system with and without SHCHE for the climatic condition of Erzurum having cold climate in Turkey.An experimental set-up,described in the next section,is constructed and tested on the basis of a university study.The coefficient of performance of the heat pump and the overall system is computed from the measurements and,the energy consumption of the ground source heat pump system in heating season is calculated.2.Experimental procedure and measurementThe ground source heat pump system presented here is at Erzurum,Turkey,latitude:39.55 N;longitude:41.16 E;placed on the East Anatolian Region of Turkey.Table1gives the climatic data for Erzurum.A schematic overview of the system is illustrated in Fig.1.The compressor(4)used for the heat pump system is a hermetic scroll type,which is driven by a2610Watt electrical motor.The heat pump has an evaporator(12)and condenser(5);both of which are water cooled plate type heat exchanger.These equipments have been insulated entirely with25mm thick rubber foam against heat loss.As shown in Fig.1,the system consists of a vertical ground heat exchanger(3)located to the depth of2Â53m,a heat pump with water-to-refrigerant heat exchanger,water circulating pumps(1) and other conventional equipments.In the system,the heat transferfluid(antifreeze-water mixture of50%)which comes from the underground goes to the water-source evaporator of the heat pump where it releases some energy,and then,it is sent to the ground heat exchangers by a water circulating pump.However, during the day,the heat transferringfluid that comes from the evaporator of the heat pump is sent to the ground.Refrigerant134a was used as workingfluid.The vertical ground heat exchanger (GHE)unit is a single U-tube placed in two vertical boreholes at the depth of53m.The pipes connecting the GHE to the evaporator were insulated and buried at the depth of2m to minimize the heat loss.In the present study,the temperatures,flow rates,pressure drops,voltages and currents were measured by appropriate instruments given in Table2.The tests were conducted ontheTable1Climatic condition of Erzurum for long-term average values.Climatic values Months in heating seasonNov.Dec.Jan.Feb.Mar.Apr.Average outdoortemperature( C)À0.5À7.2À10.8À10.1À3.7 5.2Minimum outdoortemperature( C)À6.8À12.6À16.9À16.7À9.8À0.9Maximum outdoortemperature( C)6.9À1.6À4.4À3.1 2.611.8 Average relativehumidity(%)82.081.377.573.175.056.7Average windvelocity(m/s)2.2 2.2 2.3 2.4 2.83.3Average sunshineduration(h)4.3 2.3 3.0 3.8 4.45.9Average solarradiation(MJ/m2.day)8.87.08.912.616.017.0K.Bakirci,D.Colak/Energy44(2012)996e1004997ground source heat pump system in the heating period of 2010.The measurements were taken from 8.00a.m.to 18.00p.m.with an interval of 30min.The temperatures measured by the thermo-couples were monitored in a computer and recorded by a data-acquisition card in each second,which was later used for analysis.The electronic counter (digital power meter)was used to measure the power consumption of the compressor and,the power consumptions of the pumps were measured by a watt-meter.All the measuring processes of the temperatures were monitored and controlled by a personal computer-based data-acquisition system.2.1.Uncertainty analysisExperimental errors and uncertainties can result from instru-ment selection,instrument condition,instrument calibration,environment,observation and reading and test planning.The uncertainty analysis is needed to prove the accuracy of the exper-iments [22].An uncertainty analysis was performed using a method described by Holman [23].The total uncertainties of the measurements are estimated to be Æ1.01%for the water and the antifreeze-water solution tempera-tures,Æ2.05%for pressures,Æ1.00%for power inputs to theab cr e t n u o c c i n o r t c e l E .81r e v i e c e R .7le n a p l o r t n o C .91re y r D .89. Sight glass 20. NTC temperature indicator 10. Solenoid valve 21. Data acquisition card 11. Expansion valve22. Computer and monitorGround levelFig.1.a)A schematic representation of the system (without SHCHE)b)A schematic representation of the heat pump with SHCHE and c)Outside views of the heat pump.K.Bakirci,D.Colak /Energy 44(2012)996e 1004998compressor andÆ3.00%for the circulating pumps.The uncertainty in reading values of the table is assumed to beÆ0.20%.The total uncertainties associated with massflow rate of the water and antifreeze-water solution are estimated to beÆ7.15%.The total uncertainties associated with energy received from the condenser ð_Q conÞand with heat extracted from the groundð_Q groÞareÆ7.23%. The total uncertainties associated with the COP and COPS areÆ7.30 andÆ7.28%,respectively.3.Climate properties and environment3.1.Weather dataThe experimental ground source heat pump system was estab-lished and tested in Erzurum province having an altitude of1869m and the coldest climate in Turkey.The climatic conditions of Erzurum for long-term average values(monthly average minimum, maximum and mean outdoor temperature,the monthly averages of relative humidity,wind velocity,solar radiation and sunshine durations for the heating season)are given in Table1.The annual heating and cooling degree days for Erzurum with a base temper-ature of18 C are found to be4870[24].The hours of the smallest temperature bin ofÀ19.5 C(À21 C/À18 C)observed for Erzurum in the East Anatolia Region of Turkey are17in January and February.Also,the hours of the temperature bin fromÀ21 C to18 C for Erzurum are7498in the average of 1995e2005.This procedure can account for the part-load perfor-mance of heating,ventilating and air-conditioning equipment as well as for the varying performance of heat pump systems and primary HVAC equipment[25].3.2.Soil characteristicsErzurum is an intermountain sedimentary basin with a Miocene-Quaternary volcanic basement,andesitic e basaltic lava flows andfissure eruptions lava.The ground structure in the city centre of Erzurum is predominantly alluvial structure until the thickness of1km from surface.Also,the ground structure of the city centre is gravel,sand and a little clay.The locality of Palandoken (in the south of the Centre)is the volcanic rock pieces consisting of basalt.The locality of Sanayi(in the west of the Centre)is sand,thin gravel and a little clay sometimes and,the locality of Dadaskent(in the east of the Centre)is thin sand and clay[18].3.3.EnvironmentIn general,CO2emissions are high as fossil fuels are used in our country.The heat pumps consume less primary energy than conventional heating systems and,they are an important tech-nology for reducing emissions of gases that harm the environ-ment[5].The heat pump systems are the most efficient form of electric heating,providing two to three times more heating than the equivalent amount of energy they consume in electricity. Significant emission reductions are available through the application of the heat pump system(HPS)in both residential and commercial buildings[26].Residential fossil fuel heating systems produced anywhere from1.2to36times the equivalent CO2emissions of the HPS.The CO2emission reductions from15% to77%were achieved through the use of the HPS[27].It is known that the heat pumps significantly reduce the CO2emis-sions every day whilst they provide central and domestic hot water heating[28].The heat pumps offer the most energy-efficient way to provide heating and cooling in many applica-tions,as they can use renewable heat sources in our surround-ings[29].4.Energy analysisThe measured values such as the temperature changes of the water and the antifreeze-water solution,theflow rates and the electrical power input were used to determine the performance of the system.The useful heat obtained from the condenser_Q con is calculated as,_Qcon¼_m w c wðT cwoÀT cwiÞ(1)The extracted heat from the ground is given by the following equation;_Qgro¼_m aw c awðT eaiÀT eaoÞ(2)where_m w and_m aw are theflow rate of the water in the condenser and the antifreeze-water solution in the evaporator,respectively. The COP(the heat pump)is calculated as;COP¼_Qcon_Wcom(3)The COPS(the overall system)is calculated as;COPS¼_Qcon_WcomþP_W p(4)The power input to a circulating pump_W p is computed from the following equation;_Wp¼I p V p cosðfÞ(5)where I p is the current of the pump,V p is the voltage of the pump and cos(f)is the power factor.Table2Instruments used in the system for measurements.Instrument MeasurementRotameter The massflow rates of the antifreeze-watersolution(approximately50%)Copper-constantan thermocouples The temperature of the antifreeze-water solution entering and leaving the ground heat exchanger,the inlet water temperature to and exit water temperature from heating unitBourdon-type manometers The pressures of the condenser andevaporatorMeteorological station The outdoor air temperatures and humidity Wattmeter The electrical power input to the circulatingpumpElectronic counter Instantaneous power consumptions of thecompressorNTC(negativetemperature coefficient) sensor The ground temperature at the depth of53mK.Bakirci,D.Colak/Energy44(2012)996e10049995.Results and discussionsIn this study,the performance of the ground source heat pump system with vertical ground heat exchanger wasexperimentally analyzed in Erzurum,Turkey.The experimental results were obtained in the heating season of 2010.January and February are the coolest months of the heating season in the region.Therefore,the experimental data were given only for these months.The technical details of the experimental set-up are given in Table 3.Fig.2shows the variations in the inlet-outlet tempera-tures of the heat transfer fluids to the evaporator and the condenser with time of day for the systems with and without SHCHE.As seen in Fig.2,while the temperature of the condenser outlet (T cwo )for January varies in the band of 49.6e 61.0 C,it varies in the band of 47.9e 51.4 C for February during the exper-iments carried out with SHCHE.The same temperature for January and February varies in the band of 47.7e 53.0 C and 47.2e 50.2 C,respectively,during the experiments carried out without SHCHE.Fig.2shows also the hourly variations of the inlet temperatures of the evaporator.The inlet temperatures of the evaporator have the maximum value in local time of 08:00for all the experimental conditions.Fig.3shows the variations in the condenser power,the GHE (evaporator)power and the compressor power with the time of day for the systems with and without SHCHE.Fig.4shows the daily variations of the ground temperature at the depth of 53m for the systems with and without SHCHE.As seen in Fig.4,the average ground temperatures for the systems with and without SHCHE are 6.6and 6.5 C for January,respectively.These temperatures for the systems with and without SHCHE are 5.7and 5.8 C for February,respectively.20304050607008:0010:0012:0014:0016:0018:00Time of dayT e m p e r a t u r e (°C )ba20304050607008:0010:0012:0014:0016:0018:00Time of dayT e m p e r a t u r e (°C )With (Jan. 20) and without (Jan. 23) SHCHE With (Feb. 05) and without (Feb. 03) SHCHE-10-50510152008:0010:0012:0014:0016:0018:00Time of dayT e m p e r a t u r e (°C )-10-50510152008:0010:0012:0014:0016:0018:00Time of dayT e m p e r a t u r e (°C )Fig.2.Variations in inlet-outlet temperatures with time of day for the systems with and without SHCHE,for a)Evaporator and b)Condenser.Table 3Technical details of the experimental set-up.Location :Erzurum,Turkey (lat.39.55 N;long.41.16 E)Weather information (yearly average values)Average outdoor temperature ( C) 4.7Minimum outdoor temperature ( C)À2.8Maximum outdoor temperature ( C)12.2Average relative humidity,(%)64.6Average sunshine duration (h)6.4Average solar radiation (MJ/m 2.day)15.6Average wind velocity (m/s)2.7Ground heat exchanger information TypeVertical Diameter (mm)32Deep (m)2Â53Heat pump information Capacity (kW)7Compressor type Hermetic scroll Evaporator type Plate Condenser typePlateCompressor power input (kW) 2.61(3.5HP)Capacity of cooling (kW)5.7Maximum discharge pressure (bar)29Compressor displacement (m 3/h)9.4Refrigerant typeR-134aK.Bakirci,D.Colak /Energy 44(2012)996e 1004100002468Time of dayC o n d e n s e r p o w e r (k W )a02468Time of dayC o n d e n s e r p o w e r (k W )02468Time of dayG H E (e v a p o r a t o r ) p o w e r (k W )b024680Time of dayG H E (e v a p o r a t o r ) p o w e r (k W )02468Time of day C o m p r e s s o r p o w e r (k W )c0246808:0010:0012:0014:0016:0018:0008:0010:0012:0014:0016:0018:008:0010:0012:0014:0016:0018:0008:0010:0012:0014:0016:0018:008:0010:0012:0014:0016:0018:0008:0010:0012:0014:0016:0018:00Time of dayC o m p r e s s o r p o w e r (k W )With (Jan. 20) and without (Jan. 23) SHCHE With (Feb. 05) and without (Feb. 03) SHCHEFig.3.Daily power values of the systems with and without SHCHE,for (a)Condenser power,(b)GHE (evaporator)power and (c)Compressor power.024********08:0010:0012:0014:0016:0018:00Time of dayG r o u n d t e m p e r a t u r e (°C )0246810121408:0010:0012:0014:0016:0018:00Time of dayG r o u n d t e m p e r a t u r e (°C )With (Jan. 20) and without (Jan. 23) SHCHE With (Feb. 05) and without (Feb. 03) SHCHEFig.4.Daily variations of the ground temperature at the depth of 53m for the systems with and without SHCHE.K.Bakirci,D.Colak /Energy 44(2012)996e 10041001Fig.5shows the values of the performance coef ficient of the heat pump (COP)and overall system (COPS)versus time of day for the systems with and without SHCHE.As shown in Fig.5,the values of the COP for the systems with and without SHCHE vary from 2.1to 2.7and from 2.4to 2.6in January,while they change from 2.6to 3.3and from 2.7to 3.3in February,respectively.Additionally,the values of the COPS for the systems with and without SHCHE vary from 1.9to 2.5and from 2.1to 2.3in January,while they change from 2.4to 3.1and from 2.5to 3.1in February,respectively.The average values of the COP for the systems with and without SHCHE are calculated to be 2.31and 2.47in January,while they are calculated to be 2.73and 2.81in February,respectively.The average values of the COPS for the systems with and without SHCHE are also calculated to be 2.07and 2.19in January,while they are calculated to be 2.55and 2.62in February,respectively.The variations in the inlet-outlet temperature differences (T eai ÀT eao )of the antifreeze-water solution to the GHE unit with time of day for the systems with and without SHCHE are given in Fig.6.The daily average values of the measured data and calculated results are given in Table 4.These values consist of the average values of the measurements of 21recorded from 8.00a.m.to 18.00p.m.with an interval of 30min.As seen in Table 4,the condensation pressures in average are about 15bar and,this value is very reasonable because the maximum discharge pressure limit of the compressor is 29bar.012345608:0010:0012:0014:0016:0018:00Time of dayC O Pa012345608:0010:0012:0014:0016:0018:00Time of dayC O P012345608:0010:0012:0014:0016:0018:00Time of dayC O P Sb012345608:0010:0012:0014:0016:0018:00Time of dayC O P SWith (Jan. 20) and without (Jan. 23) SHCHE With (Feb. 05) and without (Feb. 03) SHCHEFig.5.Performance coef ficients versus time of day for the systems with and without SHCHE,for a)Heat pump and b)Overall system.0246808:0010:0012:0014:0016:0018:00Time of dayT e a i -T e a o (°C )0246808:0010:0012:0014:0016:0018:00Time of dayT e a i -T e a o (°C )With (Jan. 20)and without (Jan. 23)SHCHE With (Feb. 05)and without (Feb. 03)SHCHEFig.6.Variations in inlet-outlet temperature differences (T eai ÀT eao )of the antifreeze-water solution to the GHE unit with time of day for the systems with and without SHCHE.K.Bakirci,D.Colak /Energy 44(2012)996e 100410026.ConclusionsThe performance of a vertical ground source heat pump system was investigated experimentally.In the study,the experimental results were given for the months of January and February in the heating season of2010.The experimental results indicate that the average values of the COP and the COPS are approximately2.31and 2.07with SHCHE and2.47and2.19without SHCHE in January, while they are approximately2.73and2.55with SHCHE and2.81 and2.62without SHCHE in February,respectively.Additionally,the results show that the systems with and without SHCHE are not very different in terms of the coefficient of performance but the system with SHCHE can be preferred for higher condenser outlet temperature.The heat pump systems are environmentally friendly.The initial costs of the heat pump systems are higher,but they have low operating,maintenance,and life cycle costs and a longer life expectancy than most conventional systems.Also,the heat pump systems provide heating,cooling and hot water in many applications.The ground source heat pump systems present tremendous environmental benefits when compared to the conventional systems.Therefore,these systems can be used to minimize environmental impacts and air emission. 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Jan.23,2010Feb.03,2010Unit Totaluncertainty(%)Measured parametersEvaporation pressure 2.64 2.59BarÆ2.05Condensation pressure14.7714.69BarÆ2.05Temperature of refrigerantat the compressor inlet2.35 1.52 CÆ1.01Temperature of refrigerantat the condenser inlet81.2781.31 CÆ1.01Temperature of refrigerantat the condenser outlet48.4347.73 CÆ1.01Temperature of refrigerantat the evaporator inletÀ7.83À8.24 CÆ1.01Condensing temperature54.6054.38 CÆ1.01Evaporating temperatureÀ2.95À3.46 CÆ1.01Flow rate of antifreeze-watersolution in the evaporator0.2880.333kg sÀ1Æ7.15Flow rate of water in theheating unit or thecondenser0.2670.324kg sÀ1Æ7.15Indoor air temperature11.749.73 CÆ1.01Current of circulating pumpat the GHE0.600.60AÆ1.00Current of circulating pumpat the heating unit0.690.69AÆ1.00Two-phase voltage220.0220.0VÆ1.00Temperature ofantifreeze-water solutionat the evaporator inlet1.74 1.11 CÆ1.01Temperature ofantifreeze-water solutionat the evaporator outletÀ2.30À2.65 CÆ1.01Supply water temperatureof the heating unit49.5648.41 CÆ1.01Return water temperatureof the heating unit45.1144.68 CÆ1.01Power input to the compressor 2.00 1.85kWÆ1.00Calculated parametersPower input to the circulatingpump at the GHE0.1190.119kWÆ3.00Power input to the circulatingpump at the heating unit0.1370.137kWÆ3.00Heating load of the condenser 4.955 5.207kWÆ7.23Cooling load of the evaporator 3.602 3.907kWÆ7.23Heating COP(the heat pump) 2.470 2.809eÆ7.30Heating COPS(the overall system) 2.190 2.621eÆ7.28K.Bakirci,D.Colak/Energy44(2012)996e10041003。