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## Modelling of non-equilibrium turbulent flows

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**Modelling of non-equilibrium turbulent flows**Tania S. Klein Second Year PhD Student Supervisors: Prof. Iacovides and Dr. Craft School of MACE, The University of Manchester**Outline of Presentation**• Introduction • Test Cases • Turbulence Models • Results • Conclusions**Introduction**Non-equilibrium flows: those subjected to rapid changes Sudden contraction, sudden expansion Imposed pressure gradients They are commonly found in the industry: Valves, pumps, heat exchangers, curve surfaces Objective of this work: Test different turbulence models for several cases in order to evaluate their performance.**Test Cases**• Fully Developed Channel Flow • Homogeneous Constant Shear Flow • Zero Pressure Gradient Boundary Layer • Adverse Pressure Gradient Boundary Layer • Favourable Pressure Gradient Boundary Layer • Contraction/Expansion Flows**Fully Developed Channel Flow**• One of the simplest flows: • 2D • DP=cte • U=U(y) Simulated Cases ERCOFTAC database Kawamura Lab**Homogeneous Constant**Shear Flow S=dU/dy=cte U = U(y) not wall-bounded unsteady**Zero Pressure Gradient**Boundary Layer Simulated Cases • Still a simple flow: • 2D • DP=0 • U=U(x,y)**Adverse Pressure Gradient Boundary Layer**• Non-equilibrium flow: • 2D • DP > 0 • U=U(x,y) • dU/dx < 0 S&J M&P**Favourable Pressure Gradient Boundary Layer**• Non-equilibrium flow: • 2D • DP < 0 • U=U(x,y) • dU/dx > 0 • reaches a self-similar prolife**Contraction/Expansion Flows**• Non-equilibrium flow: • 3D • dV/dy = cte • dW/dz = -cte a= 0 a= /2**Turbulence Models***Run with the wall function of Chieng and Launder (1980)**Results**Fully Developed Channel Flow General Conclusions • All models predicted the log law reasonably well. • All models predicted the shear Reynolds Stress reasonably well. • The HJ and TC models best predicted the normal Reynolds stresses.**Results**Fully Developed Channel Flow Re = 6500**Results**Fully Developed Channel Flow Re = 6500**Results**Fully Developed Channel Flow Re = 41441**Results**Homogeneous Constant Shear Flow General Conclusions • Difficult prediction • Overall, the SG and the KS model performed best • The extreme shear values are more difficult to predict. S=20√2 ; S0+=1.68 S=10 ; S0+=16.76**Results**Homogeneous Constant Shear Flow S=20√2 S0+=1.68**Results**Homogeneous Constant Shear Flow S=20√2 S0+=30.75**Results**Zero Pressure Gradient BL General Conclusions • The tested turbulence models have shown to be sensitive to the inlet conditions, implying bad predictions at low Req values. • The normal Reynolds stresses were better predicted by the RST models, as expected. • One can notice the importance of LRN models for the near wall region predictions.**Results**Zero Pressure Gradient BL**Results**Zero Pressure Gradient BL**Results**Adverse Pressure Gradient BL • The BL parameters (Cf, d, d*, q and H) were reasonably well predicted by all turbulence models. • The U and uv profiles were captured by all turbulence models up to station T5 in the S&J case. The same has not occurred for the M&P cases. • The RST models best predicted the normal Reynolds stresses, however the best model varies from case to case; station to station… General Conclusions**Results**Adverse Pressure Gradient BL S&J**Results**Adverse Pressure Gradient BL M&P**Results**Adverse Pressure Gradient BL M&P**Results**Favourable Pressure Gradient BL General Conclusions • The turbulence model which overall better predicted these flows was the KS model, although it failed to predict the Reynolds stresses. • The KS and LS models are the only ones expected to correctly predict the laminarization process, since they possess a term which accounts for the second derivative of the mean velocities. • The RST models best predicted the normal Reynolds stresses, specially the TC and HJ models.**Results**Favourable Pressure Gradient BL K=1.5x10-6**Results**Favourable Pressure Gradient BL K=1.5x10-6**Results**Favourable Pressure Gradient BL K=2.5x10-6**Results**Favourable Pressure Gradient BL K=2.5x10-6**Results**Contraction/Expansion Flows General Conclusions • No turbulence model was able to correctly predict the interruption of the applied strains. • Overall, the GL and the TC models provided the best predictions. • The eddy viscosity formulations clearly failed to predict these flows.**Results**Contraction/Expansion Flows T&R**Results**Contraction/Expansion Flows G&M - a = /2**Conclusions**• The Channel flow, which is the simplest flow, was reasonably well predicted by all turbulence models as well as the ZPGBL cases at high Req values. • The two not wall-bounded cases – HCS flow and C/E flows – were the most difficult to predict and the RST models performed better, showing the importance of calculating the Reynolds stresses through transport equations. • The APGBL cases could not be well predicted by any model at high DP, however the FM model could match the U profile. • The FPGBL cases were better predicted by the KS model which evidenced the importance of a velocity second derivative term to predict laminarization.