MODELLING OF SCROLL MACHINES: GEOMETRIC, THERMODYNAMICS AND CFD METHODS

Transcription

1 2 nd International Seminar on ORC Power Systems October 7 th & 8 th, 2013 De Doelen, Rotterdam, NL MODELLING OF SCROLL MACHINES: GEOMETRIC, THERMODYNAMICS AND CFD METHODS M. Morini, C. Pavan, M. Pinelli, E. Romito, A. Suman Dipartimento di Ingegneria Università degli Studi di Ferrara (Italy)

2 Introduction The ORC systems are becoming more common for the exploitation of energy sources with low enthalpy and for very small size applications (<10 kwel) The scroll fluid machine seems to be suitable for this applications due to: - the small number of moving parts - low noise and vibrations Higher efficiency standards could be achieved by specific studies on: kinematic thermodynamic spiral geometry, flank and axial gaps play a key role on the final performances CFD simulations could represent a very new useful method 2/14

3 Aims & Issues Geometric comparison between two methods for the design of the scroll spiral profiles Thermodynamic comparison of the two scroll compressor by evaluating overall performances Implementation of a CFD transient simulation with Dynamic Mesh strategy Sensitivity analysis on time discretization in terms of overall performance and fluid dynamic phenomena 3/14

4 Geometrical methods Both the two methods are obtained by a Involuted Circle method curvature radius spiral the spiral curve radius varies with a linear law starting from a base circumference centered in the origin of the reference system base circumference Method 1* Non-Linear Method (NLM) equations governed by non-linear coefficients Method 2** Linear Method (LM) equations governed by linear coefficients * Liu, Y. et al., 2012, Optimum design of scroll profiles created from involute of circle with variable radii by using finite element analysis, Mech. Mach. Theory, 55, pp ** Blunier, B. et al., 2006, Novel Geometrical Model of Scroll Compressors for the Analytical Description of the Chamber Volumes, ICEC 2006, /14

5 Method 1 Non Linear Method (NLM) Outer spiral Fixed scroll equations x f,out = a out cosφ + ρ out senφ y f,out = a out senφ ρ out cosφ Mobile scroll equations x m,out = x f,out + r ob sinθ y m,out = y f,out r ob cosθ Coefficients (outer) a out = a o + δ 0 φ + α k ρ out = a o φ + α + δ 0 k + 1 φ + α k+1 Inner spiral x f,in = a in cosφ + ρ in senφ y f,in = a in senφ ρ in cosφ x m,in = x f,in + r ob sinθ y m,in = y f,in r ob cosθ Coefficients (inner) a in = a 0 + δ 0 (φ π + α) k ρ in = a o φ α + δ 0 k + 1 φ + α π k+1 (π 2α) k+1 where: a 0 base circumference radius, orbit angle and r ob orbit radius defined as: r ob = a 0 π 2α δ 0 (π 2α)k+1 k + 1 The coefficents k, δ 0 allow to control the spiral thickness variation: k = distance between the inner and outer spiral δ 0 = variation of the spiral thickness as function of θ 5/14

6 Method 2 Linear Method (LM) Outer spiral x f,out = a 0 (cosφ + φsenφ) Fixed scroll φ y f,out I f,out = a[α 0 (senφ out,s, φ max φcosφ) ] Mobile scroll x m,out = a 0 cos φ + π + φ sen φ + π + r ob cos (θ + 3π 2) y m,out = a 0 sen φ + π φ cos φ + π + r ob sen (θ + 3π 2) Inner spiral x f,in = a 0 [cos φ + α i0 + φsen φ + α i,0 ] Fixed scroll φ y f,in I f,in = = a 0 [sen α in,s φ + α i0 α i0, φ max φcos αφ i0 + α i,0 ] Mobile scroll x m,in = a 0 cos φ + α i0 + π + φ sen φ + α i0 + π + r ob cos (θ + 3π 2) y m,in = a 0 sen φ + α i0 + π φ cos φ + α i0 + π + r ob sen (θ + 3π 2) Perfectly Meshing Profile*** (PMP) connect the inner and outer profile. The PMP influence the spiral geometry, leakage and structural resistance *** Liu, Y. et al., 2010, Study on involute of circle with variable radii in a scroll compressor, Mech. Mach. Theory, 45, pp /14

7 Comparison All the geometric features influence the overall performance of the scroll Method 1 - NLM fixed spiral Method 2 - LM mobile spiral Volume ratio = 2.47 The end-plate of the scroll is less than the diameter obtained by the LM method* Volume ratio = 2.53 The distance between the inner and outer spiral is lower than the NLM method* * for given base circumference radius, blade height, involute ending angle and inner spiral initial angle 7/14

8 V c [m 3 ] Thermodynamic analysis T [K] p [Pa] Simplified thermodynamic model of an energy balance in an open control volume: no heat exchange constant fluid properties at inlet and outlet sections air ideal standard conditions partial derivatives approximated by finite differences ΔT = 1 Δθ m c v T Δp ΔV = 1 T R 1 ΔV c ΔT v Δθ c v V c Δθ 4.5E E E E E E E E E E+00 LM NLM θ [ ] LM NLM θ [ ] Same performance, different mass flow rate 8/14

9 CFD analysis LM numerical model CFD peculiarity: 2D transient simulations by using a Dynamic Mesh strategy can reproduce the real operation of the machine through a sequence of different positions by imposing an angular increment Δθ Mesh with local refinement 302,000 tetrahedral elements regenerated each time step MAX skewness < 0.47 min orthogonal q.lty > 0.68 Inlet Pa Scroll fixed casing 2D numerical domain with adiabatic wall Outlet Pa Mesh deformation closely related to the step amplitude Δθ 4 different Δθ Δθ = Δθ = Δθ = Δθ = /14

10 CFD analysis Global pressure DM strategy = pressure increment during the scroll orbit θ = 0 θ = π/2 θ = π θ = 3/2 π Pressure [kpa] Compression chambers Noise & vibrations imbalanced load for the mobile spiral with different pressure due to the asymmetric inlet position 10/14

11 CFD analysis Local pressure Δθ = Velocity [m/s] higher pressure Δθ = Δθ = control point Δθ = Δθ = Δθ = Δθ = Δθ = Δθ = local solution affected by Δθ and the turbulence model (k-ε) wide recirculation zones with reversed flow are present at the inlet section 11/14

12 CFD analysis Mass flow rate Mass flow inlet for the2 nd and 3 rd orbit Δθ = Δθ = Δθ = Δθ = The Δθ = simulation presents greatest fluctuations Every Δθ shows the same trend of the mass flow rate The global mass flow rate was affected by the flank leakage due to the flank gap (equal to 78 μm for the LM Scroll geometry) 12/14

13 CFD analysis Flank leakage The flank gap (equal to 78 μm) determines the leakage that reduce the volumetric efficiency Velocity [m/s] Δθ = from the suction chamber to the external volume (casing) of the scroll compressor from the compression chamber to the suction chamber of the scroll compressor 13/14

14 Conclusions The geometric methods analyzed showed significant differences in geometric structure of the scroll compressor, while the overall performance (in terms of compression ratio, temperature, ) were the same A CFD method was developed by means of a transient Dynamic Mesh strategy The sensitivity analysis showed that overall performances are not influenced by the Δθ, but local mesh deformation can lead to different local fields of pressure and velocity CFD simulations allowed the evaluation of time profile of the mass flow rate and pressure fluctuations in every point of the domain study and optimization of the shape of the spiral profile study and optimization of the shape and the position of inlet and outlet ducts analysis and optimization of the noise and vibration of the ORC system 14/14