pressure (drop) Konference ANSYS 2011 A steady state approach to calculation of valve pressure rise rate characteristics Ján Oravec Technical centre, Sauer-Danfoss a.s., Považská Bystrica joravec@sauer-danfoss.com Abstract: Pressure relief valves are widely used in hydrostatic circuits. The pressure rise rate characteristics are one of the most important descriptions of the valves performance. This article proposes design of the basic pressure rise rate characteristic of valve using only a few CFD calculations. These calculations are performed for several poppet strokes and flow values. The method is shown for charge pressure relief valve but can be used similarly for any poppet type valve. Keywords: pressure relief valve, hydrostatics, pressure rise rate characteristic, CFD 1. Introduction Pressure relief valves are essential components in hydrostatic systems. They protect the systems against excessive pressures or maintain pressures at desired levels. The performances of such valves are represented by their pressure rise rate characteristics. A simplified one is shown in Fig. 1. Note, the valve remains closed while pressure is lower than the cracking pressure. If the pressure exceeds the cracking pressure, p cr, the valve opens to allow escaping of working fluid (hydraulic oil) to a reservoir. A small slope of the characteristic is desired in standard working range of the valve. If the poppet reaches its maximal stroke limit, the valve behaves like a constant orifice for higher flow rates. Because each the point of the characteristic represents different poppet stroke (also flow, pressure ), the standard calculation (as well as real measurement) leads to transient task including remeshing and solution of equation of motion. cracking pressure (p cr ) poppet at maximal stroke flow rate Fig. 1. Simplified pressure rise rate characteristic
TechSoft Engineering & SVS FEM If we take into account some simplifications: dynamic effects are avoided, valve at fixed poppet stroke behaves like an orifice which has quadratic function behavior for wide range of flow rates, we can design the valve characteristic from several CFD steady state calculations. This approach is shown for charge pressure relief valve. spring pretension mechanism nut with guide R guide pump end cap outlet channel connected to pump case case pressure marked by blue (p case ) R seat springs balance chamber poppet gallery (channel) charge pressure marked by red (p charge ) inlet branch of the gallery for measurement as well as CFD purposes these branches are closed for measurement as well as CFD purposes Fig. 2. Design of charge pressure relief valve
Konference ANSYS 2011 2. Charge pressure relief valve (CPRV) The function of CPRV is to maintain charge pressure of the closed hydrostatic system at a designated level above case pressure (Sauer-Danfoss, 2011). The CPRV is a direct acting poppet valve (Fig. 2). It opens and discharges fluid to the pump case when pressure exceeds the designated level, p charge, at a channel called gallery. The valve poppet has a cone which acts against a seat created in the pump end cap (Fig. 2). The poppet guiding is provided by a guide designed in the nut. The 2 springs provide force which acts in direction to close the valve. Pretension of one spring can be adjusted by a bolt to reach desired level of the cracking pressure. The pretension force can be calculated from equation: 2 2 F 0 = p cr R seat R guide π, (1) where p c = p carge p case and radii R seat, R guide are evident from Fig. 2. As the poppet moves, the spring force corresponds to equation: F spring = F 0 + k s, (2) where k is spring rate and s is poppet stroke. 3. CFD model As mentioned above, the steady state approach is used here. The CFD models (Fig. 3) are prepared for 3 poppet strokes (0.5 mm, 1.5 mm and 3 mm). There is used combination of hexahedral, tetrahedral and wedge mesh types created using ANSYS ICEM CFD. The CFD analysis is performed in ANSYS Fluent. Material properties of hydraulic oil Shell Tellus 46 are used. The fluid is assumed as incompressible. Based on previous investigation, experience and comparison with testing, laminar model is chosen in this specific case. Pressure outlet boundary condition is applied to the pump housing passage. The pressure p out = p case is constant for all the calculated cases. Velocity inlet boundary condition is experienced as suitable and stable for this task. Inlet velocity and flow rate are related to each other by simple relation: q = q in = v in A in, (3) where q in is inlet flow rate, v in is inlet velocity magnitude and A in is inlet area. The velocity magnitude (flow rate respectively) is ramped to several values for each the stroke model. At least, 3 discrete velocity magnitudes are needed for each the stroke to be able approximate results by quadratic function. As a result from each the CFD calculation is: pressure at inlet (p in ), flow force induced by oil to the poppet (F). For reference, pressure contours and streamlines in region of control passage are shown in Fig. 4 for 1 mm poppet stroke and 70 l min -1 flow rate case.
limits are set manually TechSoft Engineering & SVS FEM poppet modeled at 3 stroke positions detail of hexahedral mesh in control passage area pressure outlet (p case ) velocity inlet Fig. 3. CFD model Fig. 4. Pressure contours and streamlines in control passage region (1 mm stroke, 70 l min -1 flow)
Konference ANSYS 2011 4. Post-processing The post-processing plays big role in this task. We have data from 9 CFD calculations (3 strokes 3 flow rates per each stroke = 9 calculations) in this specific example. Therefore further data processing in a spreadsheet or other suitable tool is needed. The input and output values can be collected into a table form for further processing. One table proposal is following: stroke flow rate pressure drop flow force s q p = p in p out F Tab. 1. Proposed table for collection of CFD inputs and outputs The visualization of data points can be seen in Fig. 5. The triangle points in graph C represent dependency of the pressure drop on flow rate. The different colors relate to different poppet strokes. Similarly, the square points in graph B represent dependency of the flow force on flow rate. The data points can be approximated by quadratic polynomial trendlines (continuous colored lines in graphs B and C) for each the stroke value. The flow force at constant stroke can be then written in form: F = a q 2 + b q + c, (4) where a, b, and c are polynomial coefficients obtained from the spreadsheet trendline properties. It is obvious the flow force has to be in balance with the spring force (2) at each the point of final pressure rise rate characteristic. Therefore we can write: Solution of this quadratic equation is: F = F spring a q 2 + b q + c F spring = 0 (5) q s = b± b2 4 a c F spring 2 a, (6) where the sign plus or minus is chosen in way to obtain physically correct result. So, using (6) we get flow rate at which there is balance between flow force and spring force at constant stroke (compare graphs A and B in Fig. 5 to see balance between spring force and flow force for each the stroke).
TechSoft Engineering & SVS FEM C s 1 =const. p s1 p cr q s1 A B s 1 =const. s 1 Fig. 5. Visualisation of the pressure rise rate characteristic design Similarly to the flow forces approximation, we can also approximate the pressure drop data points using quadratic polynomial trendlines in form: p = d q 2 + e q + f, (7) where the polynomial coefficients d, e, and fare obtained again from the spreadsheet trendline properties. If we use the calculated flow rate from (6), we obtain corresponding pressure drop: p s = d q s 2 + e q s + f, (8) This procedure is repeated for all the 3 strokes so we obtain the flow rate and pressure drop pairs: q s1, p s1, q s2, p s2, q s3, p s3 (9) plus we have the additional point q s0 = 0, p cr. The final pressure rise rate characteristic can be designed from those points see red line in graph C in Fig. 5. 5. Comparison with measurement A simplified hydraulic scheme used for measurement of the CPRV is shown in Fig. 6a. An auxiliary pump H provides oil to the testing device. The throttle valve TV is fully open so the pressure indicated by the gauge G1 is small in comparison with the cracking pressure of the tested CPRV. As the TV restricts flow area, the load of
Konference ANSYS 2011 CPRV increases and it starts to operate. Pressure before CPRV (G1) and behind it (G2) is recorded together with flow rate (Q). Note the measurement process should be sufficiently slow to avoid dynamic effects of the system. It is possible to perform measurement of the CPRV installed in a simple test block or installed in the pump end cap. The measured valve performance with the one calculated by CFD are shown in Fig. 6b for comparison. G1 G2 CPRV TV Q H a b Fig. 6. Measurement hydraulic scheme (a) and comparison CFD with measurement (b) 6. Conclusion The design of pressure rise rate characteristic of charge pressure relief valve using steady state CFD simulation is shown in the article. The model is prepared for 3 constant strokes. Minimally 3 different flow rate conditions needs to be calculated for each the stroke due to possibility of data approximation by quadratic polynomial functions. Both pressure drop and flow force functions are approximated in relation to flow rate. The final pressure rise rate characteristic of the valve is found using condition of equilibrium of flow force and spring force at each the specific stroke. Because of computing only a few steady state cases, the proposed method saves computing time as well as effort to set up the analysis in comparison to transient CFD computation. Another advantage is the effect of the cracking pressure or spring rate change is re-calculated immediately in the spreadsheet without any additional CFD calculation requirement. 7. Bibliography 1. H1 Axial Piston Pumps Single and Tandem, Basic Information, Sauer-Danfoss, 11062168-Rev BB-Apr 2011. 2. Imre M., Kriššák P., Rahmfeld R., Zavadinka P., Porovnanie simulačných a meraných výsledkov škrtiaceho ventila, Hydraulika a pneumatika, 1-2/2010, ISSN 1335-5171.