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A three-dimensional flow model of screen channel liquid acquisition devices for propellant management in microgravity

A three-dimensional flow model of screen channel liquid acquisition devices for propellant... www.nature.com/npjmgrav ARTICLE OPEN A three-dimensional flow model of screen channel liquid acquisition devices for propellant management in microgravity 1,4 1,2,4✉ 1 2,3 2,3 2,3 1,2 Zheng Wang , Guang Yang , Ye Wang , Xin Jin , Rui Zhuan , Hao Zhang and Jingyi Wu Screen channel liquid acquisition devices (LADs) are among the most promising technologies for separating liquid and vapor phases in propellant storage tanks under microgravity conditions and thus ensuring vapor-free propellant supply to spacecraft engines. However, the prediction of the critical flow rate of a screen channel LAD relies on the full understanding of the three dimensional distribution of injection velocity. In this study, the flow characteristics at the entrance region of the LAD were investigated via particle image velocimetry (PIV) technique and numerical simulations under various working conditions. The experimental results illustrated that the velocity component normal to the porous woven mesh is non-uniform in both streamwise and spanwise directions of channel flow and that this phenomenon has a significant influence on the critical flow rate. Hence, a model that accounts for the three-dimensional flow field was proposed to predict the critical flow rate. The average error in the critical flow rate, which was determined by comparing the proposed model’s predictions and the experimental results, was less than 8.4%. npj Microgravity (2022) 8:28 ; https://doi.org/10.1038/s41526-022-00216-5 INTRODUCTION bubble point pressure was dominated by the liquid temperature, since higher surface tensions could be usually obtained at lower Due to the absence of acceleration under microgravity condi- temperatures. tions , it is challenging to guarantee vapor-free supply of The flow-through-screen pressure drop (ΔP ) refers to the propellant from a tank to an orbital spacecraft. The situation is FTS pressure loss that occurs when liquid flows across a wetted porous even more serious for cryogenic propellants e.g., liquid oxygen woven mesh. Modeling-based ΔP prediction has been studied FTS (LOX) and liquid hydrogen (LH ), since their low boiling 17,18 extensively for decades , with related experiments conducted temperatures may accelerate evaporation and the fluids in the 2–4 for both room-temperature and cryogenic fluids, including LH , storage tank are usually in two-phase states . In order to ensure 2 19,20 18 LN , and H O . Armour and Cannon developed an empirical effective propellant transportation, capillary-driven propellant 2 2 model that treated the porous woven mesh as a thin packed bed. management devices (PMDs) such as vanes, sponges, and screen 21,22 1,4–6 McQuillen et al. conducted a series of numerical studies to channel liquid acquisition devices (LADs) , which take full explore LAD performances in various orientations and submersion advantage of surface tension to separate vapor and liquid depths based on the assumptions made by Armour and Cannon . continuously without consuming excess energy, have been Hartwig et al. investigated LH and LOX pressure distributions proposed. Among these, screen channel LADs are the most 2 inside the LAD channel experimentally. The results showed that promising approach due to their applicability at relatively high 2,7,8 the flow-through-screen (FTS) pressure drop is related to flow rates and under adverse acceleration . When a screen temperature and increases significantly at lower temperatures. channel LAD operates, the liquid is driven by a pressure difference Thereafter, Wang et al. developed an analytical model for the to flow through a porous woven mesh and down to an outlet. At FTS pressure drop that considers the effects of pore structures on the same time, the liquid within the microscopic mesh pores the flow. generates a capillary force that blocks vapor passage into the A higher bubble point pressure requires a smaller pore channel. Thus, the screen channel LAD can ensure that single- diameter; conversely, a system with a lower FTS pressure drop phase liquid is supplied to the engines. prefers a larger pore size. There is an inherent trade-off between The bubble point pressure (ΔP ) and flow-through-screen BP the FTS pressure drop and bubble point pressure when choosing pressure drop (ΔP ) are two critical parameters that govern LAD FTS 9–11 the porous woven mesh. Therefore, it is necessary to achieve a separation performance . The bubble point pressure is the minimum pressure difference required for the vapor to break compromise between these two parameters in order to optimize through the porous woven mesh and the flow rate at this pressure the LAD design. Previous studies focused mainly on porous woven mesh performance. Although some device-level experiments have is defined as the critical flow rate. Experimental and theoretical been conducted using LADs , the results focused on operational analyses have verified a simplified bubble point model based on the Young–Laplace equation for room-temperature fluids and parameters, such as the flow rate and breakdown condition. 4,12–15 saturated cryogenic fluid states . In general, the bubble point Furthermore, due to the complexity of porous media flow, most of is determined from the effective pore diameter, surface tension the traditional models assume a uniform injection velocity along and contact angle . The relevant relationship is expressed as the LAD channel, which results in an overprediction of the critical 16 23 ΔP  4γ cos θ =D . In addition, Hartwig et al. found that the flow rate. Hartwig et al. proposed a one-dimensional (1D) BP c p 1 2 Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China. Joint Laboratory for Cryogenic Propulsion Technology of Aerospace 3 4 Systems, Shanghai 200240, China. Aerospace System Engineering Shanghai, Shanghai 201109, China. These authors contributed equally: Zheng Wang, Guang Yang. email: y_g@sjtu.edu.cn Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; Z. Wang et al. steady-state model that assumed that the injection velocity was mentioned in the Methods section. For a given porous woven uniform throughout the porous woven mesh. The results were mesh, a higher outflow rate results in a larger velocity magnitude reported to overpredict performance by 18% compared with at the entrance region, and generates a larger velocity difference actual anti-gravity liquid acquisition tests. They also pointed out as well. that a two-dimensional (2D) or three-dimensional (3D) model is The injection velocity v at the centerline (x = 105 mm, required to estimate the injection velocity distribution along the y = 83 mm, z from 70 to 140 mm) before the porous woven mesh LAD channel accurately. Among the limited studies that con- was extracted from the captured images to study the velocity sidered the non-uniformity of injection velocity, Hartwig and variation at the entrance region, as shown in Fig. 4. In order to 25 26 Darr and Darr et al. derived a mathematical solution from the evaluate the velocity distributions in different cases the velocity 2D Navier–Stokes equations to predict the pressure drop was scaled, and the normalized velocity v was defined as follows: distribution along the channel. Their 2D model was found to v ¼ v=v ; (1) avgcenter perform better than the previous 1D model. However, the velocity non-uniformity in the spanwise direction has not been taken into where v is the line-averaged injection velocity at avgcenter consideration. Moreover, there is still a lack of experimental data y = 83 mm and x = 105 mm, which can be calculated using regarding the 3D injection velocity distribution to support the v ¼ vdz =H. avgcenter available theoretical models. Therefore, a detailed experimental x¼W=2 The results indicate that the normalized injection velocity investigation of flow dynamics through the porous woven mesh of increases approximately linearly along the outflow direction in all a screen channel LAD is of great significance. cases, as shown in Fig. 4a–c. Therefore, a non-uniformity In order to solve the aforementioned problems, we investigated coefficient δ is utilized to describe the non-uniformity of the the characteristics of flow through the porous woven mesh of a injection velocity at unit length in z-direction quantitatively, screen channel LAD under various working conditions using particle image velocimetry (PIV) and numerical simulations. The v  v m avgcenter detailed 3D velocity fields at the entrance region of the screen δ ¼ ; (2) wetted channel LAD are experimentally obtained. Based on the analysis of the velocity distribution, we propose a 3D flow model that can where v is the normalized maximum injection velocity while more accurately predict the critical flow rate of the screen v is the normalized line-averaged injection velocity, and avgcenter channel LAD. H is the length of the porous woven mesh that contacts the wetted bulk liquid in the tank. The injection velocity non-uniformity for the entire fluid entrance region is calculated as δ  H . Figure 4a–c wetted RESULTS shows that δ  H varies by less than 3%, when the flow rate is wetted −1 The velocity field in the liquid acquisition system changed in the range of 20–43 L h for each porous mesh. To evaluate the influence of mesh types on the injection velocity To investigate the fluid dynamics through the porous woven mesh distribution, the injection velocity non-uniformity is calculated for of the screen channel LAD, an anti-gravity liquid acquisition test 80 × 700 DT, 130 × 1100 DT, and 165 × 1500 DT meshes. As system was implemented. The system consisted of a test tank, a presented in Fig. 4d, the velocity non-uniformity decreases as PIV facility, and a data acquisition system. Figure 1a, b presents a the pore diameter increases. The injection velocity produced using schematic of the experimental system. The recorded areas on xy an 80 × 700 DT (the largest pore size) is more uniform than that and yz planes using the PIV technique are illustrated in Fig. 1c. experienced with the smallest pore size (165 × 1500 DT). This also Three types of Dutch Twill screens were used in the experiments agrees with theoretical analysis (Supplementary Discussion). Other (Supplementary Fig. 2), and their properties are shown in Table 1. parameters affecting the velocity non-uniformity include the fluid Details on the theoretical basis, materials, experimental setup, and properties, size, shape, and surface roughness of the LAD channel the data acquisition and reduction procedure are presented in the (Supplementary Discussion, Supplementary Equation 14). Methods section. Figure 2 shows a typical velocity field at the yz plane for the −1 80 × 700 DT mesh at Q = 43 L h by experiments. The distribution Distribution of injection velocity in the spanwise direction of the injection velocity illustrates that the fluid flows towards the y In order to explore the injection velocity distribution in the direction in zone I and then flows across the porous woven mesh. spanwise direction, the velocity field at xy planes of different Afterwards, the fluid flows in the channel towards the outflow port height levels is also experimentally analyzed. Figure 5 shows the at the top of the channel. It is obvious that the velocity in zone II velocity distribution with a 90% fill level for 80 × 700 DT at −1 (inside the channel) is one order of magnitude larger than that in Q = 43 L h . The velocity field at different height levels shows zone I (the entrance region outside the channel) due to the large that the injection velocity close to the channel outlet is generally ratio between the inlet area of the submerged mesh and the cross- larger than that near the dead-end of the LAD channel, which is in section of the channel. The velocity magnitude increases along the accordance with the results shown in Fig. 2. Moreover, the y and z directions in zone I and zone II and reaches its maximum experimental results indicate that the injection velocity at the near the outflow port inside the channel wall. The increase in the middle of porous mesh is also larger than that near the side walls injection velocity in the z-direction results in a reduction of the in x direction, which is a clear evidence that the injection velocity critical flow rate, which is discussed further in this work. in x direction is also non-uniform. Similarly, a dimensionless scale factor λ could be utilized to quantitatively describe the non- Distribution of injection velocity in the streamwise direction uniformity of the injection velocity in x-direction, which is calculated as follow: Velocity distributions for the various meshes and flow rates at the 0 1 0 1 yz plane are shown in Fig. 3. All of the flow fields exhibit similar Z ZZ ZZ B C B C characteristics in zone I. In particular, the velocity at the entrance B C B C λ ¼ vdz=H  vdxdz=WH = vdxdz=WH : (3) @ 0  x  W A @ 0  x  W A x¼W=2 region increases along the z direction. For each case, higher values 0  z  H 0  z  H of velocity magnitude are mainly distributed in the vicinity of the mesh, and the velocity decreases rapidly with the increasing distance to the mesh. This also proves that the distance between The difference between the injection velocity at x = W/2 and the porous wall and the inner wall of the tank has little effect on the average velocity at the whole inlet can be obtained from the the inlet velocity distribution if it is larger than 10 mm, as velocity field. npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; Z. Wang et al. Fig. 1 The anti-gravity liquid acquisition test system. a Photograph, b top-view schematic of the test tank when measuring the velocity at the yz plane, and c areas recorded using the PIV technique (dashed rectangles at the yz and xy planes). The recorded yz plane was divided into three zones. Zone I was the entrance zone, zone II was the channel zone, and zone III was the supply zone. Table 1. Properties of porous woven mesh. Mesh type 80 × 700 DT 130 × 1100 DT 165 × 1500 DT Shute wire diameter 76 48 33 (μm) Wrap wire diameter (μm) 101 68 61 Porosity ε 0.370 0.369 0.418 Hydraulic pore diameter 46.5 29.7 26.9 D (μm) Effective pore diameter 53.4 ± 5.8 35.2 ± 3.7 29.9 ± 3.1 D (μm) Specific surface area S 31842 49731 62148 −1 (m ) −1 24 6 6 6 A (m )ofEq. (13) 6.4 × 10 10.1 × 10 6.9 × 10 Fig. 2 The distribution of the velocity vector at yz plane for the B of Eq. (13) 13 13 7 −1 80 × 700 DT mesh at Q = 43 L h . The velocity in zone II is generally one order of magnitude larger than that in zone I. Numerical simulations of the injection velocity field In order to analyze the 3D flow behaviors in detail, numerical simulations of single-phase outflow in the LAD channel were Furthermore, a second-order upwind scheme was used to performed. The computational domain was half (H = 200 mm, discretize the momentum terms. The inlet and outlet conditions L = 15 mm, W = 7.5 mm) of the LAD channel with surrounding were set as the pressure-inlet and mass-flow-outlet, respectively. liquids, which is symmetrical at the vertical plane denoted by All of the solid walls are set as no-slip walls. The simulations were x = 105 mm. The governing equations were solved using a run using commercial CFD software, ANSYS Fluent. pressure-based SIMPLE algorithm and steady implicit formulation. The porous-jump model was used for the porous woven mesh since the mesh is thin (less than 1 mm) and the fluid flow is Since the pore-scale Reynolds number (Re ¼ ρu=μS D ) was perpendicular to the mesh. In this model, the pressure gradient in smaller than 1 and the channel-scale Reynolds number ( the porous woven mesh is described using Re ¼ ρuW=μ) was smaller than 1000 for the range of parameters 27,28 considered in this work, the laminar flow model was used . The dp=dy ¼ D μv þ ρC v =2; (4) second order scheme was used for pressure discretization. y y Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28 Z. Wang et al. Fig. 3 The velocity distribution in zone I at yz plane for various flow rates and porous woven mesh types. First row: 80 × 700 DT, second −1 −1 −1 row: 130 × 1100 DT, third row: 165 × 1500 DT. First column: Q= 20 (±3) L h , second column: Q= 32 (±3) L h , third column: Q= 43 (±3) L h . Fig. 4 The distribution of normalized injection velocity for various porous woven meshes at different flow rates. a 80 × 700 DT, b 130 × 1100 DT, and c 165 × 1500 DT. d Injection velocity non-uniformity for various types of porous woven mesh (The error bar indicates the standard deviation of four independent experiments). npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA Z. Wang et al. Fig. 5 The distribution of injection velocity at different height levels. a z = 160 mm b z = 100 mm c z= 40 mm. That is, the velocity magnitude increases in the z direction along the channel and the injection velocity profile is approximately parabolic in the x direction. Simulated and experimentally determined injection velocity distributions along the z direction at the entrance region are compared in Fig. 7a for the flow rate of −1 Q = 43 L h and 80 × 700 DT mesh. The simulation results and experimental data exhibit a similar tendency as both increase along the z direction. The experimentally determined injection velocity non-uniformity in z direction is ~17.2%, while the simulation result is about 8.7%. The velocity distribution in the z direction from the present study is also found to be of the same trend but slightly more non-uniform as compared to that derived from the 2D Navier-Stokes equations . (Supplementary Methods). The discrepancy between the experiment and simulation might be caused mainly by the assumption that the inner wall of the LAD channel is smooth in the simulations. Since the friction loss is smaller in the simulation, a smaller injection velocity non- uniformity would be observed. (Supplementary Discussion, Supplementary Equation 14) The distributions of injection velocity in x direction at z = 40 mm, 100 mm, and 160 mm from the experiments and simulations are extracted and presented in Fig. 7b for the flow rate −1 of Q = 43 L h and 80 × 700 DT mesh. The average difference between experiments and simulations is about 3.4%, which further verified the present numerical model. Experimental results in Fig. 7b indicate that the non-uniformity factor of the injection Fig. 6 Typical velocity distributions at the entrance region and velocity in x-direction, i.e., λ as defined in Eq. (3), changes slightly inside the LAD channel by numerical simulation. The velocity at various height levels, which are 19.2%, 18.5%, and 18.4% at magnitude increases in the z direction along the channel and the injection velocity profile is approximately parabolic in the x direction. z = 160 mm, 100 mm and 40 mm, respectively. The value of λ is −1 16.0% as calculated from the simulation results at Q = 43 L h with 80 × 700 DT mesh, which is close to the experiments. The where D is the viscous resistance coefficient and C is the inertial y y value of λ was also found to be less sensitive to the variation of the resistance coefficient . The pressure gradient inside the porous specification of the mesh. woven mesh is treated as constant, so the FTS pressure drop can be calculated as Effect of injection velocity field on the critical flow rate ΔP ¼ D μv þ ρC v =2 Δm; (5) FTS y y As the injection velocity of the screen-channel LAD is non-uniform in both x and z directions, its effect on the critical flow rate is where Δm is the thickness of the porous woven mesh . According analyzed. When the critical maximum injection velocity is to Eq. (5), three parameters must be determined in order to use recorded as the average injection velocity, which is the so-called the porous-jump model: the face permeability 1=D , the porous 1D model, the critical flow rate of a screen channel LAD is medium thickness Δm, and the porous-jump coefficient C . calculated as follows: Equations (13) and (5) can be used to calculate these parameters for each porous mesh via the analytical model . A total of Q ¼ v  A : (6) cr1D max c 1.4 × 10 hexahedral cells were used in all cases. Grid indepen- where A is the effective flow area of the porous woven mesh and dence was confirmed by changing the number of cells from 6 6 v is the maximum injection velocity on A under the critical max c 1.4 × 10 to 1.8 × 10 and observing that the velocity deviation condition that the total pressure loss equals the bubble point was smaller than 1%. pressure. To consider the injection velocity non-uniformity in the Typical velocity distributions at the entrance region and inside z-direction, i.e., 2D flow model , the velocity in Eq. (6) should be the LAD channel by the numerical simulations are shown in Fig. 6. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28 Z. Wang et al. −1 Fig. 7 The distribution of injection velocity for simulation and experiments at Q = 43 L h with 80 × 700 DT mesh. a Injection velocity at yz plane, b injection velocity at xy plane. design, the 3D model, which considers the injection velocity non- uniformity in both z and x directions, performs the best in predicting the critical flow rate. The average deviations between the 3D, 2D, and 1D models and the experiments are 8.4%, 16.7%, and 48.5%, respectively. It should be noted that the non-uniformity coefficients may be influenced by the geometry of the channel and the working fluids, which should be further analyzed in the future. Nevertheless, the present results prove that the velocity distributions in both streamwise and spanwise directions of the channel flow affect the critical flow rate of the screen channel LAD, and neglecting the 3D injection effect would overpredict the critical flow rate. The influence of gravity In order to quantify the influence of gravity, simulation cases for single-phase outflow in the LAD channel were tested at −2 g = 0ms . Figure 9 shows the velocity distributions in the LAD channel from the experiment and from simulations at −2 −2 g = −9.8 m s and g = 0ms . For single-phase flow, gravity z z Fig. 8 The critical flow rates in different prediction models and has little influence on the velocity distribution inside the channel. experiments. (The error bar indicates the standard deviation of four However, the critical flow rate is reduced under normal gravity independent experiments). due to hydrostatic pressure loss (Supplementary Equation 4). Moreover, microgravity changes the distribution of the vapor and optimized by the line-averaged injection velocity using the liquid phases outside the channel. Liquid tends to gather near the aforementioned non-uniformity coefficient δ. The average injec- tank walls and vapor tends to concentrate in the middle of the tank . tion velocity in a 2D model can be written as Therefore, the middle of the LAD channel is more likely to be max v ¼ : avgcenter (7) exposed to vapor, which introduces a slight change in the velocity δ  H þ 1 wetted distribution in the channel. For a wetted porous woven mesh in continuous contact with bulk liquids, the non-uniformity coefficient Then the critical flow rate by a 2D model is calculated as follows can also be utilized directly to evaluate the average injection velocity. Q ¼ v  A : (8) cr2D avgcenter c In the region exposed to vapor, there is no mass transported and the pressure decreases mainly due to friction loss. Therefore, the Moreover, the non-uniformity coefficient λ in the x-direction can injection velocity non-uniformity could be enlarged by the random be utilized to optimize the average injection velocity further by vapor-liquid interface. Nevertheless, the injection velocity non- considering the 3D flow. According to Eqs. (3) and (7), the face- uniformity still plays a major role in the overall pressure distribution averaged injection velocity in the 3D model can be expressed as inside the channel, and on-ground experimental investigation v v avgcenter max provides essential guidance for the design of screen channel LADs v ¼ ¼ : (9) avg λ þ 1 ðÞ λ þ 1ðÞ δ  H þ 1 wetted for on-orbit missions . Then the critical flow rate as predicted by a 3D model is calculated as follows DISCUSSION In summary, we investigated the flow characteristics at the Q ¼ v  A : (10) cr3D avg c entrance region of a screen channel liquid acquisition device (LAD) in this study. An anti-gravity liquid acquisition system Figure 8 compares the critical flow rates predicted by these comprising a test tank, PIV facility, and data acquisition system models and that measured by experiments. The non-uniformity was built. The influences of various meshes (80 × 700 DT, coefficients are determined from the injection velocity fields as −1 discussed above, and their values corresponding to the experimental 130 × 1100 DT, 165 × 1500 DT) and flow rates (0–60 L h ) were condition are listed in Supplementary Table 5. In the experiments, investigated in detail. Numerical simulations of single-phase −2 the critical flow rate is determined as the flow rate when the first outflow in the LAD channel were also conducted at g = 0ms −2 bubble flows across the mesh. With regard to the LAD channel and g = −9.8 m s using a porous-jump model for the porous npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA Z. Wang et al. −1 −2 Fig. 9 The velocity distribution in the LAD channel for 80 × 700 DT at Q = 43 L h .a Experiment, b simulation at g = −9.8 m s , and −2 c simulation at g = 0ms . woven mesh. The injection velocity non-uniformity in the x and z Based on the present study, we also suggest reducing the injection directions were studied in detail, and a prediction model was velocity non-uniformity by improving the LAD design. Possible proposed to evaluate the critical flow rate of the screen channel approaches include optimizing the position of the LAD channel LAD based on the three-dimensional injection flow fields. The outlet, optimizing the geometry of the LAD channel, and using main conclusions are as follows: combinations of porous woven mesh types. Moreover, outflow tests using various fluids, with various channel sizes, for a larger range of (1) For single-phase liquid flow, the injection velocity is almost flow rates, and under microgravity conditions, should be conducted perpendicular to the porous woven mesh. The velocity in future work to validate and improve the present model further. increases along the channel flow direction and reaches its maximum near the outlet. In the spanwise direction, the velocity distribution is of approximately parabolic profile. METHODS (2) Experimental results indicate that porous woven meshes with Theoretical basis smaller pores produce less uniform injection velocities along The primary parameters that govern LAD performance are the the channel flow direction. The maximum injection velocity bubble point pressure and the total pressure loss. The bubble point non-uniformity may reach 30% for a 165 × 1500 DT mesh. In 29,30 pressure can be expressed using the Young–Laplace equation, thespanwisedirection,the velocity is not sensitive to the variation of the mesh specification. For the flow rate range ΔP ¼ 4γcosθ =D ; (11) BP c p considered in this study, the variation of flow rate has a where γ is the surface tension of the fluid; θ is the contact angle; negligible influence on velocity non-uniformity in both and D is the effective pore diameter of the porous woven mesh. directions. The total pressure loss inside the LAD channel should be less (3) A 3D model was proposed to predict the critical flow rate of than ΔP to prevent vapor penetration into the channel. For the BP the screen channel LAD, which considers the injection velocity experiments of Fig. 1a, The total pressure loss (ΔP ) is total non-uniformity in both streamwise and spanwise directions. expressed as The results of the 3D model were compared to experimental data to reveal an error of less than 8.4%, which indicates that ΔP ¼ ΔP þ ΔP þ ΔP þ ΔP þ ΔP ; total hydrostatic FTS friction dynamic other the model is reasonable. In particular, the accuracy of the 3D (12) modelismuchbetterthanthatofthe 1D and2Dmodels. (4) Microgravity influences the location of the vapor-liquid where ΔP is the hydrostatic pressure in the LAD channel, hydrostatic interface due to the dominance of the capillary force. Thus, ΔP is the FTS pressure drop, ΔP is the frictional loss inside FTS friction the middle of the LAD channel may be more likely to be the LAD channel, ΔP is the dynamic pressure drop, and dynamic exposed to vapor in microgravity conditions. However, ΔP is the pressure loss caused by vibration and fluid sloshing. other simulation results indicate that gravity has little influence on In microgravity environments, ΔP dominates the pressure loss FTS the velocity distribution for the wetted region and inside the term and influences the operational efficiency directly since the channel for single-phase flow. hydrostatic pressure is negligible . Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28 Z. Wang et al. According to Wang et al. , the FTS pressure drop can be pore geometries. The relevant parameters and the geometric expressed as properties of the test meshes are listed in Table 1. The PIV system (LaVision Inc.) included a high-speed camera ΔP ¼ A μv þ B ρv ; (13) FTS p p (4008 × 2672 pixels) and a laser pulse generator (Nd:YAG LASER NANO TRL, 425 mJ at 532 nm and 10 Hz). Particle motion was where A and B are FTS coefficients, which are determined by the p p captured by operating the high-speed camera at 2 Hz. The test geometry of the porous woven mesh; μ is the fluid viscosity; and ρ tank and the areas recorded using the PIV technique were shown is the fluid density. in Fig. 1c. The recorded area at yz plane starts at x = 105 mm, The maximum allowable liquid flow flux is referred to as the y = 5 mm, and z = 60 mm. With a 90% fill level, the vapor-liquid critical flow rate (Q ) and occurs when the total pressure loss is equal cr interface and channel bottom were located at z = 180 mm and to the bubble point pressure (ΔP ¼ ΔP ). Since the traditional total BP z = 0 mm, respectively. The laser was mounted perpendicular to 1D model assumes that the velocity across the porous woven mesh 10,23,25,31 the porous woven mesh at x = 105 mm, and thus the camera is uniform , the critical flow rate of the LAD could be captured particle motion across the yz plane of the porous mesh. calculated usind Eq. (6). However, recent studies have indicated a Due to the limited field-of-view, the size of the area recorded by large disparity between the critical flow rate derived from the 1D and the camera was limited to 80 × 165 mm. To test the spanwise experimental data, since the distribution of the fluid injection velocity distribution, three xy planes at z = 40 mm, 100 mm and velocity at the porous mesh plays an important role in the critical 160 mm were recorded. The orientations and positions of the flow rate, but was less considered in the previous studies . high-speed camera and the laser pulse generator were adjusted accordingly. Deionized water was chosen as the test fluid Experimental setup −3 −1 (ρ = 998.2 kg m , μ = 1.002 mPa s, and γ = 72.8 mN m ). Prior All the outflow tests of screen channel LAD were conducted in a to the experiments, water was doped with particles with transparent test tank made from quartz glass, a material that −3 diameters of 9 μm and density of 1.1 g cm , so that the particles’ exhibits good chemical stability and excellent optical properties volume fraction is around 0.002%. At such low concentrations, the (Supplementary Fig. 1). The size of the tank was 200 × 200 × tracking particles have been verified to have no obvious effect on 210 mm . The upper side of the test tank was a stainless-steel the water properties, including density, surface tension and plate affixed to the LAD channel with epoxy resin. It could also be 34,35 viscosity (<5%) . Experiments were conducted to recheck the removed from the test tank so that the LAD channel could be difference in bubble point pressures and contact angles between replaced and tests run under different conditions. The test system deionized water and doped water. The difference in bubble point −2 was placed at ground level with g = −9.8 m s . pressures was found to be within the experimental uncertainty. The LAD channel was a hollow duct composed of three The contact angle of deionized water and doped water show the transparent walls and a porous wall made from porous metal same value of 71 (±2)° on the stainless-steel plate (Supplementary mesh. The LAD channel was 15 mm long (L), 15 mm wide (W), and Fig. 3). Preliminary analysis also indicated that the particles would 200 mm high (H). The porous wall of the LAD channel was 85 mm not obviously clog the porous woven mesh during the tests away from the inner wall of the tank. Preliminary experiments (Supplementary Fig. 4) . A peristaltic pump was used to drain indicated that the distance had a negligible effect on the critical water from the channel and pumping it back into the test tank to flow rate provided that the distance was larger than 10 mm, as the maintain the fill level. The flow rate of the peristaltic pump could pressure loss caused by the distance between the porous wall and also be adjusted to achieve different working conditions. the inner wall is much smaller than the other items in Eq. (12). The bottom of the LAD channel is about 5 mm away from the wall of Data acquisition and reduction the tank. Considering the injection velocity is parallel to the Experiments were conducted at different flow rates for each type bottom wall, and the velocity magnitude is very low at the dead- of woven porous mesh. All of the test cases were repeated four end region, the distance is assumed to have no significant effect times to verify the consistency and repeatability, with each test on the LAD performance . Assembly of the LAD channel conducted at the steady state. The images captured using the proceeded as follows. Prior to the test, the porous woven mesh camera were analyzed via a cross-correlation algorithm using the was cleaned in an ultrasonic cleaner using alcohol and deionized LaVision PIV module and post-processed in MATLAB. The pressure water. The porous woven mesh was affixed to the channel using drop was detected using a pressure difference sensor with a range epoxy resin to avoid sealing and delamination at the edges. Two of 0–20 kPa. The flow rate was detected using two flow meters differential pressure transducers were mounted 25 mm apart at −1 −1 the bottom and top of the channel, as shown in Fig. 1c. with ranges of 4–40 L h and 40–400 L h , respectively. The Dutch Twill screens were used in the experiments since this uncertainty of the pressure difference sensor is 0.075%, while the type of mesh offers the smallest pore diameter and the most uncertainty of the flow rate is 1.5%. The diameter of particles is tortuous flow path. These features can prevent vapor ingestion . 1.7–1.9 pixels in the tracking images, and the measurement Three porous woven meshes with different pore sizes were uncertainty is between 0.05 and 0.1 px . Therefore, the uncer- chosen as experimental materials: an 80 × 700 Dutch Twill (DT) tainty of the PIV-derived velocity vectors is below 5.9%. mesh, a 130 × 1100 DT mesh, and a 165 × 1500 DT mesh. The porous meshes are labeled in the form n ´ n , where n and n w s w s Reporting summary denote the number of warp and shute wires per inch, respectively. Further information on research design is available in the Nature Prior to the experiments, the bubble point pressures of the Research Reporting Summary linked to this article. meshes were tested , and the effective pore diameter D was obtained based on Eq. (11) (Supplementary Methods, Supple- mentary Tables 2–4). The effective pore diameters overlap with DATA AVAILABILITY historical values considering the uncertainties caused by All data generated or analyzed during this study are included in this published article measurement and manufacturing. The diameters of wrap and and its supplementary information files. shute wires were obtained from scanning electron microscopy (SEM, by TESCAN VEGA3) images as shown in Supplementary Fig. 2, while the porosity ε, specific surface area S , hydraulic pore CODE AVAILABILITY diameter D (=4ε/S ), and the FTS pressure coefficients in Eq. (13) The code used to generate the plots are available from the corresponding author on h v were calculated according to the method of Wang et al. from the reasonable request. npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA Z. Wang et al. Received: 6 January 2022; Accepted: 13 July 2022; 29. Hartwig, J. & Mann, J. A. A predictive bubble point pressure model for porous liquid acquisition device screens. J. Porous Media 17, 587–600 (2014). 30. Hartwig, J., McQuillen, J. & Jurns, J. Screen channel liquid-acquisition-device bubble point tests in liquid oxygen. J. Thermophys. 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Cryogenic Propellants (SKLTSCP202005) and Shanghai Sailing Program 10. Hartwig, J. & Darr, S. Influential factors for liquid acquisition device screen selec- (20YF1447900). tion for cryogenic propulsion systems. Appl. Therm. Eng. 66, 548–562 (2014). 11. Ma, Y., Zimnik, D., Dreyer, M. & Li, Y. Investigation on cryo-wicking performance within metallic weaves under superheated conditions for screen channel liquid AUTHOR CONTRIBUTIONS acquisition devices (LADs). Int. J. Heat. Mass Transf. 141, 530–541 (2019). 12. Adamson, A. W. & Gast, A. P. Physical Chemistry of Surfaces. Vol. 150 (Interscience Z.W.: Numerical simulations, Experiments, Analysis, Writing—original draft. G.Y.: publishers New York, 1967). Conceptualization, Experiments, Methodology, Writing—review & editing. Y.W.: 13. Jurns, J. M. & Hartwig, J. W. Liquid oxygen liquid acquisition device bubble point Experiments, Writing—review & editing. X.J.: Validation, Writing—review & editing. tests with high pressure lox at elevated temperatures. Cryogenics 52,283–289 (2012). R.Z.: Resources, Writing – review & editing. H.Z.: Writing—review & editing. J.W.: 14. Hartwig, J., Chato, D. & McQuillen, J. Screen channel LAD bubble point tests in Writing—review & editing, Project administration. liquid hydrogen. Int. J. Hydrog. Energy 39, 853–861 (2014). 15. Yi, T. et al. Dynamics of a gas bubble penetrating through porous media. Phys. Fluids 34, 012103 (2022). COMPETING INTERESTS 16. Hartwig, J. W. et al. Screen channel liquid acquisition device outflow tests in The authors declare no competing interests. liquid hydrogen. Cryogenics 64, 295–306 (2014). 17. Chhabra, R. P. & Richardson, J. F. Flow of liquids through screens: Relationship between pressure drop and flow rate. Chem. Eng. Sci. 40, 313–316 (1985). ADDITIONAL INFORMATION 18. Armour, J. C. & Cannon, J. N. Fluid flow through woven screens. AIChE J. 14, Supplementary information The online version contains supplementary material 415–420 (1968). available at https://doi.org/10.1038/s41526-022-00216-5. 19. Blatt, M., Start, J. & Siden, L. Low Gravity Propellant Control Using Capillary Devices in Large Scale Cryogenic Vehicles. Design Handbook GDC-DDB70-008 (1970). Correspondence and requests for materials should be addressed to Guang Yang. 20. Ludewig, M., Omori, S. & Rao, G. Pressure Drop Across Woven Screens Under Uniform and Nonuniform Flow Conditions. Alabama Univ., Huntsville Report (1974). Reprints and permission information is available at http://www.nature.com/ 21. McQuillen, J. B. et al. Porous screen applied in liquid acquisition device channel reprints and CFD simulation of flow in the channel. J. Porous Media 15, 429–437 (2012). 22. Zhang, N., Chato, D. J., McQuillen, J. B., Motil, B. J. & Chao, D. F. CFD simulation of Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims pressure drops in liquid acquisition device channel with sub-cooled oxygen. in published maps and institutional affiliations. World Acad. Sci., Eng. Technol. 58, 1180–1185 (2009). 23. Hartwig, J. W., Darr, S. R., McQuillen, J. B., Rame, E. & Chato, D. J. A steady state pressure drop model for screen channel liquid acquisition devices. Cryogenics 64, 260–271 (2014). Open Access This article is licensed under a Creative Commons 24. Wang, Y. et al. Analytical model of flow-through-screen pressure drop for metal Attribution 4.0 International License, which permits use, sharing, wire screens considering the effects of pore structures. Chem. Eng. Sci. 229, adaptation, distribution and reproduction in any medium or format, as long as you give 116037 (2021). appropriate credit to the original author(s) and the source, provide a link to the Creative 25. Hartwig, J. & Darr, S. Analytical model for steady flow through a finite channel Commons license, and indicate if changes were made. The images or other third party with one porous wall with arbitrary variable suction or injection. Phys. Fluids 26, material in this article are included in the article’s Creative Commons license, unless 123603 (2014). indicated otherwise in a credit line to the material. If material is not included in the 26. Darr, S. R., Camarotti, C. F., Hartwig, J. W. & Chung, J. N. Hydrodynamic model of article’s Creative Commons license and your intended use is not permitted by statutory screen channel liquid acquisition devices for in-space cryogenic propellant regulation or exceeds the permitted use, you will need to obtain permission directly management. Phys. Fluids 29, 017101 (2017). from the copyright holder. To view a copy of this license, visit http:// 27. Terzis, A. et al. Microscopic velocity field measurements inside a regular porous creativecommons.org/licenses/by/4.0/. medium adjacent to a low Reynolds number channel flow. Phys. Fluids 31, 042001 (2019). 28. Yang, G. et al. Pore-scale numerical simulations of flow and convective heat © The Author(s) 2022 transfer in a porous woven metal mesh. Chem. Eng. Sci. 256, 117696 (2022). Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png npj Microgravity Springer Journals

A three-dimensional flow model of screen channel liquid acquisition devices for propellant management in microgravity

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www.nature.com/npjmgrav ARTICLE OPEN A three-dimensional flow model of screen channel liquid acquisition devices for propellant management in microgravity 1,4 1,2,4✉ 1 2,3 2,3 2,3 1,2 Zheng Wang , Guang Yang , Ye Wang , Xin Jin , Rui Zhuan , Hao Zhang and Jingyi Wu Screen channel liquid acquisition devices (LADs) are among the most promising technologies for separating liquid and vapor phases in propellant storage tanks under microgravity conditions and thus ensuring vapor-free propellant supply to spacecraft engines. However, the prediction of the critical flow rate of a screen channel LAD relies on the full understanding of the three dimensional distribution of injection velocity. In this study, the flow characteristics at the entrance region of the LAD were investigated via particle image velocimetry (PIV) technique and numerical simulations under various working conditions. The experimental results illustrated that the velocity component normal to the porous woven mesh is non-uniform in both streamwise and spanwise directions of channel flow and that this phenomenon has a significant influence on the critical flow rate. Hence, a model that accounts for the three-dimensional flow field was proposed to predict the critical flow rate. The average error in the critical flow rate, which was determined by comparing the proposed model’s predictions and the experimental results, was less than 8.4%. npj Microgravity (2022) 8:28 ; https://doi.org/10.1038/s41526-022-00216-5 INTRODUCTION bubble point pressure was dominated by the liquid temperature, since higher surface tensions could be usually obtained at lower Due to the absence of acceleration under microgravity condi- temperatures. tions , it is challenging to guarantee vapor-free supply of The flow-through-screen pressure drop (ΔP ) refers to the propellant from a tank to an orbital spacecraft. The situation is FTS pressure loss that occurs when liquid flows across a wetted porous even more serious for cryogenic propellants e.g., liquid oxygen woven mesh. Modeling-based ΔP prediction has been studied FTS (LOX) and liquid hydrogen (LH ), since their low boiling 17,18 extensively for decades , with related experiments conducted temperatures may accelerate evaporation and the fluids in the 2–4 for both room-temperature and cryogenic fluids, including LH , storage tank are usually in two-phase states . In order to ensure 2 19,20 18 LN , and H O . Armour and Cannon developed an empirical effective propellant transportation, capillary-driven propellant 2 2 model that treated the porous woven mesh as a thin packed bed. management devices (PMDs) such as vanes, sponges, and screen 21,22 1,4–6 McQuillen et al. conducted a series of numerical studies to channel liquid acquisition devices (LADs) , which take full explore LAD performances in various orientations and submersion advantage of surface tension to separate vapor and liquid depths based on the assumptions made by Armour and Cannon . continuously without consuming excess energy, have been Hartwig et al. investigated LH and LOX pressure distributions proposed. Among these, screen channel LADs are the most 2 inside the LAD channel experimentally. The results showed that promising approach due to their applicability at relatively high 2,7,8 the flow-through-screen (FTS) pressure drop is related to flow rates and under adverse acceleration . When a screen temperature and increases significantly at lower temperatures. channel LAD operates, the liquid is driven by a pressure difference Thereafter, Wang et al. developed an analytical model for the to flow through a porous woven mesh and down to an outlet. At FTS pressure drop that considers the effects of pore structures on the same time, the liquid within the microscopic mesh pores the flow. generates a capillary force that blocks vapor passage into the A higher bubble point pressure requires a smaller pore channel. Thus, the screen channel LAD can ensure that single- diameter; conversely, a system with a lower FTS pressure drop phase liquid is supplied to the engines. prefers a larger pore size. There is an inherent trade-off between The bubble point pressure (ΔP ) and flow-through-screen BP the FTS pressure drop and bubble point pressure when choosing pressure drop (ΔP ) are two critical parameters that govern LAD FTS 9–11 the porous woven mesh. Therefore, it is necessary to achieve a separation performance . The bubble point pressure is the minimum pressure difference required for the vapor to break compromise between these two parameters in order to optimize through the porous woven mesh and the flow rate at this pressure the LAD design. Previous studies focused mainly on porous woven mesh performance. Although some device-level experiments have is defined as the critical flow rate. Experimental and theoretical been conducted using LADs , the results focused on operational analyses have verified a simplified bubble point model based on the Young–Laplace equation for room-temperature fluids and parameters, such as the flow rate and breakdown condition. 4,12–15 saturated cryogenic fluid states . In general, the bubble point Furthermore, due to the complexity of porous media flow, most of is determined from the effective pore diameter, surface tension the traditional models assume a uniform injection velocity along and contact angle . The relevant relationship is expressed as the LAD channel, which results in an overprediction of the critical 16 23 ΔP  4γ cos θ =D . In addition, Hartwig et al. found that the flow rate. Hartwig et al. proposed a one-dimensional (1D) BP c p 1 2 Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China. Joint Laboratory for Cryogenic Propulsion Technology of Aerospace 3 4 Systems, Shanghai 200240, China. Aerospace System Engineering Shanghai, Shanghai 201109, China. These authors contributed equally: Zheng Wang, Guang Yang. email: y_g@sjtu.edu.cn Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; Z. Wang et al. steady-state model that assumed that the injection velocity was mentioned in the Methods section. For a given porous woven uniform throughout the porous woven mesh. The results were mesh, a higher outflow rate results in a larger velocity magnitude reported to overpredict performance by 18% compared with at the entrance region, and generates a larger velocity difference actual anti-gravity liquid acquisition tests. They also pointed out as well. that a two-dimensional (2D) or three-dimensional (3D) model is The injection velocity v at the centerline (x = 105 mm, required to estimate the injection velocity distribution along the y = 83 mm, z from 70 to 140 mm) before the porous woven mesh LAD channel accurately. Among the limited studies that con- was extracted from the captured images to study the velocity sidered the non-uniformity of injection velocity, Hartwig and variation at the entrance region, as shown in Fig. 4. In order to 25 26 Darr and Darr et al. derived a mathematical solution from the evaluate the velocity distributions in different cases the velocity 2D Navier–Stokes equations to predict the pressure drop was scaled, and the normalized velocity v was defined as follows: distribution along the channel. Their 2D model was found to v ¼ v=v ; (1) avgcenter perform better than the previous 1D model. However, the velocity non-uniformity in the spanwise direction has not been taken into where v is the line-averaged injection velocity at avgcenter consideration. Moreover, there is still a lack of experimental data y = 83 mm and x = 105 mm, which can be calculated using regarding the 3D injection velocity distribution to support the v ¼ vdz =H. avgcenter available theoretical models. Therefore, a detailed experimental x¼W=2 The results indicate that the normalized injection velocity investigation of flow dynamics through the porous woven mesh of increases approximately linearly along the outflow direction in all a screen channel LAD is of great significance. cases, as shown in Fig. 4a–c. Therefore, a non-uniformity In order to solve the aforementioned problems, we investigated coefficient δ is utilized to describe the non-uniformity of the the characteristics of flow through the porous woven mesh of a injection velocity at unit length in z-direction quantitatively, screen channel LAD under various working conditions using particle image velocimetry (PIV) and numerical simulations. The v  v m avgcenter detailed 3D velocity fields at the entrance region of the screen δ ¼ ; (2) wetted channel LAD are experimentally obtained. Based on the analysis of the velocity distribution, we propose a 3D flow model that can where v is the normalized maximum injection velocity while more accurately predict the critical flow rate of the screen v is the normalized line-averaged injection velocity, and avgcenter channel LAD. H is the length of the porous woven mesh that contacts the wetted bulk liquid in the tank. The injection velocity non-uniformity for the entire fluid entrance region is calculated as δ  H . Figure 4a–c wetted RESULTS shows that δ  H varies by less than 3%, when the flow rate is wetted −1 The velocity field in the liquid acquisition system changed in the range of 20–43 L h for each porous mesh. To evaluate the influence of mesh types on the injection velocity To investigate the fluid dynamics through the porous woven mesh distribution, the injection velocity non-uniformity is calculated for of the screen channel LAD, an anti-gravity liquid acquisition test 80 × 700 DT, 130 × 1100 DT, and 165 × 1500 DT meshes. As system was implemented. The system consisted of a test tank, a presented in Fig. 4d, the velocity non-uniformity decreases as PIV facility, and a data acquisition system. Figure 1a, b presents a the pore diameter increases. The injection velocity produced using schematic of the experimental system. The recorded areas on xy an 80 × 700 DT (the largest pore size) is more uniform than that and yz planes using the PIV technique are illustrated in Fig. 1c. experienced with the smallest pore size (165 × 1500 DT). This also Three types of Dutch Twill screens were used in the experiments agrees with theoretical analysis (Supplementary Discussion). Other (Supplementary Fig. 2), and their properties are shown in Table 1. parameters affecting the velocity non-uniformity include the fluid Details on the theoretical basis, materials, experimental setup, and properties, size, shape, and surface roughness of the LAD channel the data acquisition and reduction procedure are presented in the (Supplementary Discussion, Supplementary Equation 14). Methods section. Figure 2 shows a typical velocity field at the yz plane for the −1 80 × 700 DT mesh at Q = 43 L h by experiments. The distribution Distribution of injection velocity in the spanwise direction of the injection velocity illustrates that the fluid flows towards the y In order to explore the injection velocity distribution in the direction in zone I and then flows across the porous woven mesh. spanwise direction, the velocity field at xy planes of different Afterwards, the fluid flows in the channel towards the outflow port height levels is also experimentally analyzed. Figure 5 shows the at the top of the channel. It is obvious that the velocity in zone II velocity distribution with a 90% fill level for 80 × 700 DT at −1 (inside the channel) is one order of magnitude larger than that in Q = 43 L h . The velocity field at different height levels shows zone I (the entrance region outside the channel) due to the large that the injection velocity close to the channel outlet is generally ratio between the inlet area of the submerged mesh and the cross- larger than that near the dead-end of the LAD channel, which is in section of the channel. The velocity magnitude increases along the accordance with the results shown in Fig. 2. Moreover, the y and z directions in zone I and zone II and reaches its maximum experimental results indicate that the injection velocity at the near the outflow port inside the channel wall. The increase in the middle of porous mesh is also larger than that near the side walls injection velocity in the z-direction results in a reduction of the in x direction, which is a clear evidence that the injection velocity critical flow rate, which is discussed further in this work. in x direction is also non-uniform. Similarly, a dimensionless scale factor λ could be utilized to quantitatively describe the non- Distribution of injection velocity in the streamwise direction uniformity of the injection velocity in x-direction, which is calculated as follow: Velocity distributions for the various meshes and flow rates at the 0 1 0 1 yz plane are shown in Fig. 3. All of the flow fields exhibit similar Z ZZ ZZ B C B C characteristics in zone I. In particular, the velocity at the entrance B C B C λ ¼ vdz=H  vdxdz=WH = vdxdz=WH : (3) @ 0  x  W A @ 0  x  W A x¼W=2 region increases along the z direction. For each case, higher values 0  z  H 0  z  H of velocity magnitude are mainly distributed in the vicinity of the mesh, and the velocity decreases rapidly with the increasing distance to the mesh. This also proves that the distance between The difference between the injection velocity at x = W/2 and the porous wall and the inner wall of the tank has little effect on the average velocity at the whole inlet can be obtained from the the inlet velocity distribution if it is larger than 10 mm, as velocity field. npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA 1234567890():,; Z. Wang et al. Fig. 1 The anti-gravity liquid acquisition test system. a Photograph, b top-view schematic of the test tank when measuring the velocity at the yz plane, and c areas recorded using the PIV technique (dashed rectangles at the yz and xy planes). The recorded yz plane was divided into three zones. Zone I was the entrance zone, zone II was the channel zone, and zone III was the supply zone. Table 1. Properties of porous woven mesh. Mesh type 80 × 700 DT 130 × 1100 DT 165 × 1500 DT Shute wire diameter 76 48 33 (μm) Wrap wire diameter (μm) 101 68 61 Porosity ε 0.370 0.369 0.418 Hydraulic pore diameter 46.5 29.7 26.9 D (μm) Effective pore diameter 53.4 ± 5.8 35.2 ± 3.7 29.9 ± 3.1 D (μm) Specific surface area S 31842 49731 62148 −1 (m ) −1 24 6 6 6 A (m )ofEq. (13) 6.4 × 10 10.1 × 10 6.9 × 10 Fig. 2 The distribution of the velocity vector at yz plane for the B of Eq. (13) 13 13 7 −1 80 × 700 DT mesh at Q = 43 L h . The velocity in zone II is generally one order of magnitude larger than that in zone I. Numerical simulations of the injection velocity field In order to analyze the 3D flow behaviors in detail, numerical simulations of single-phase outflow in the LAD channel were Furthermore, a second-order upwind scheme was used to performed. The computational domain was half (H = 200 mm, discretize the momentum terms. The inlet and outlet conditions L = 15 mm, W = 7.5 mm) of the LAD channel with surrounding were set as the pressure-inlet and mass-flow-outlet, respectively. liquids, which is symmetrical at the vertical plane denoted by All of the solid walls are set as no-slip walls. The simulations were x = 105 mm. The governing equations were solved using a run using commercial CFD software, ANSYS Fluent. pressure-based SIMPLE algorithm and steady implicit formulation. The porous-jump model was used for the porous woven mesh since the mesh is thin (less than 1 mm) and the fluid flow is Since the pore-scale Reynolds number (Re ¼ ρu=μS D ) was perpendicular to the mesh. In this model, the pressure gradient in smaller than 1 and the channel-scale Reynolds number ( the porous woven mesh is described using Re ¼ ρuW=μ) was smaller than 1000 for the range of parameters 27,28 considered in this work, the laminar flow model was used . The dp=dy ¼ D μv þ ρC v =2; (4) second order scheme was used for pressure discretization. y y Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28 Z. Wang et al. Fig. 3 The velocity distribution in zone I at yz plane for various flow rates and porous woven mesh types. First row: 80 × 700 DT, second −1 −1 −1 row: 130 × 1100 DT, third row: 165 × 1500 DT. First column: Q= 20 (±3) L h , second column: Q= 32 (±3) L h , third column: Q= 43 (±3) L h . Fig. 4 The distribution of normalized injection velocity for various porous woven meshes at different flow rates. a 80 × 700 DT, b 130 × 1100 DT, and c 165 × 1500 DT. d Injection velocity non-uniformity for various types of porous woven mesh (The error bar indicates the standard deviation of four independent experiments). npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA Z. Wang et al. Fig. 5 The distribution of injection velocity at different height levels. a z = 160 mm b z = 100 mm c z= 40 mm. That is, the velocity magnitude increases in the z direction along the channel and the injection velocity profile is approximately parabolic in the x direction. Simulated and experimentally determined injection velocity distributions along the z direction at the entrance region are compared in Fig. 7a for the flow rate of −1 Q = 43 L h and 80 × 700 DT mesh. The simulation results and experimental data exhibit a similar tendency as both increase along the z direction. The experimentally determined injection velocity non-uniformity in z direction is ~17.2%, while the simulation result is about 8.7%. The velocity distribution in the z direction from the present study is also found to be of the same trend but slightly more non-uniform as compared to that derived from the 2D Navier-Stokes equations . (Supplementary Methods). The discrepancy between the experiment and simulation might be caused mainly by the assumption that the inner wall of the LAD channel is smooth in the simulations. Since the friction loss is smaller in the simulation, a smaller injection velocity non- uniformity would be observed. (Supplementary Discussion, Supplementary Equation 14) The distributions of injection velocity in x direction at z = 40 mm, 100 mm, and 160 mm from the experiments and simulations are extracted and presented in Fig. 7b for the flow rate −1 of Q = 43 L h and 80 × 700 DT mesh. The average difference between experiments and simulations is about 3.4%, which further verified the present numerical model. Experimental results in Fig. 7b indicate that the non-uniformity factor of the injection Fig. 6 Typical velocity distributions at the entrance region and velocity in x-direction, i.e., λ as defined in Eq. (3), changes slightly inside the LAD channel by numerical simulation. The velocity at various height levels, which are 19.2%, 18.5%, and 18.4% at magnitude increases in the z direction along the channel and the injection velocity profile is approximately parabolic in the x direction. z = 160 mm, 100 mm and 40 mm, respectively. The value of λ is −1 16.0% as calculated from the simulation results at Q = 43 L h with 80 × 700 DT mesh, which is close to the experiments. The where D is the viscous resistance coefficient and C is the inertial y y value of λ was also found to be less sensitive to the variation of the resistance coefficient . The pressure gradient inside the porous specification of the mesh. woven mesh is treated as constant, so the FTS pressure drop can be calculated as Effect of injection velocity field on the critical flow rate ΔP ¼ D μv þ ρC v =2 Δm; (5) FTS y y As the injection velocity of the screen-channel LAD is non-uniform in both x and z directions, its effect on the critical flow rate is where Δm is the thickness of the porous woven mesh . According analyzed. When the critical maximum injection velocity is to Eq. (5), three parameters must be determined in order to use recorded as the average injection velocity, which is the so-called the porous-jump model: the face permeability 1=D , the porous 1D model, the critical flow rate of a screen channel LAD is medium thickness Δm, and the porous-jump coefficient C . calculated as follows: Equations (13) and (5) can be used to calculate these parameters for each porous mesh via the analytical model . A total of Q ¼ v  A : (6) cr1D max c 1.4 × 10 hexahedral cells were used in all cases. Grid indepen- where A is the effective flow area of the porous woven mesh and dence was confirmed by changing the number of cells from 6 6 v is the maximum injection velocity on A under the critical max c 1.4 × 10 to 1.8 × 10 and observing that the velocity deviation condition that the total pressure loss equals the bubble point was smaller than 1%. pressure. To consider the injection velocity non-uniformity in the Typical velocity distributions at the entrance region and inside z-direction, i.e., 2D flow model , the velocity in Eq. (6) should be the LAD channel by the numerical simulations are shown in Fig. 6. Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28 Z. Wang et al. −1 Fig. 7 The distribution of injection velocity for simulation and experiments at Q = 43 L h with 80 × 700 DT mesh. a Injection velocity at yz plane, b injection velocity at xy plane. design, the 3D model, which considers the injection velocity non- uniformity in both z and x directions, performs the best in predicting the critical flow rate. The average deviations between the 3D, 2D, and 1D models and the experiments are 8.4%, 16.7%, and 48.5%, respectively. It should be noted that the non-uniformity coefficients may be influenced by the geometry of the channel and the working fluids, which should be further analyzed in the future. Nevertheless, the present results prove that the velocity distributions in both streamwise and spanwise directions of the channel flow affect the critical flow rate of the screen channel LAD, and neglecting the 3D injection effect would overpredict the critical flow rate. The influence of gravity In order to quantify the influence of gravity, simulation cases for single-phase outflow in the LAD channel were tested at −2 g = 0ms . Figure 9 shows the velocity distributions in the LAD channel from the experiment and from simulations at −2 −2 g = −9.8 m s and g = 0ms . For single-phase flow, gravity z z Fig. 8 The critical flow rates in different prediction models and has little influence on the velocity distribution inside the channel. experiments. (The error bar indicates the standard deviation of four However, the critical flow rate is reduced under normal gravity independent experiments). due to hydrostatic pressure loss (Supplementary Equation 4). Moreover, microgravity changes the distribution of the vapor and optimized by the line-averaged injection velocity using the liquid phases outside the channel. Liquid tends to gather near the aforementioned non-uniformity coefficient δ. The average injec- tank walls and vapor tends to concentrate in the middle of the tank . tion velocity in a 2D model can be written as Therefore, the middle of the LAD channel is more likely to be max v ¼ : avgcenter (7) exposed to vapor, which introduces a slight change in the velocity δ  H þ 1 wetted distribution in the channel. For a wetted porous woven mesh in continuous contact with bulk liquids, the non-uniformity coefficient Then the critical flow rate by a 2D model is calculated as follows can also be utilized directly to evaluate the average injection velocity. Q ¼ v  A : (8) cr2D avgcenter c In the region exposed to vapor, there is no mass transported and the pressure decreases mainly due to friction loss. Therefore, the Moreover, the non-uniformity coefficient λ in the x-direction can injection velocity non-uniformity could be enlarged by the random be utilized to optimize the average injection velocity further by vapor-liquid interface. Nevertheless, the injection velocity non- considering the 3D flow. According to Eqs. (3) and (7), the face- uniformity still plays a major role in the overall pressure distribution averaged injection velocity in the 3D model can be expressed as inside the channel, and on-ground experimental investigation v v avgcenter max provides essential guidance for the design of screen channel LADs v ¼ ¼ : (9) avg λ þ 1 ðÞ λ þ 1ðÞ δ  H þ 1 wetted for on-orbit missions . Then the critical flow rate as predicted by a 3D model is calculated as follows DISCUSSION In summary, we investigated the flow characteristics at the Q ¼ v  A : (10) cr3D avg c entrance region of a screen channel liquid acquisition device (LAD) in this study. An anti-gravity liquid acquisition system Figure 8 compares the critical flow rates predicted by these comprising a test tank, PIV facility, and data acquisition system models and that measured by experiments. The non-uniformity was built. The influences of various meshes (80 × 700 DT, coefficients are determined from the injection velocity fields as −1 discussed above, and their values corresponding to the experimental 130 × 1100 DT, 165 × 1500 DT) and flow rates (0–60 L h ) were condition are listed in Supplementary Table 5. In the experiments, investigated in detail. Numerical simulations of single-phase −2 the critical flow rate is determined as the flow rate when the first outflow in the LAD channel were also conducted at g = 0ms −2 bubble flows across the mesh. With regard to the LAD channel and g = −9.8 m s using a porous-jump model for the porous npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA Z. Wang et al. −1 −2 Fig. 9 The velocity distribution in the LAD channel for 80 × 700 DT at Q = 43 L h .a Experiment, b simulation at g = −9.8 m s , and −2 c simulation at g = 0ms . woven mesh. The injection velocity non-uniformity in the x and z Based on the present study, we also suggest reducing the injection directions were studied in detail, and a prediction model was velocity non-uniformity by improving the LAD design. Possible proposed to evaluate the critical flow rate of the screen channel approaches include optimizing the position of the LAD channel LAD based on the three-dimensional injection flow fields. The outlet, optimizing the geometry of the LAD channel, and using main conclusions are as follows: combinations of porous woven mesh types. Moreover, outflow tests using various fluids, with various channel sizes, for a larger range of (1) For single-phase liquid flow, the injection velocity is almost flow rates, and under microgravity conditions, should be conducted perpendicular to the porous woven mesh. The velocity in future work to validate and improve the present model further. increases along the channel flow direction and reaches its maximum near the outlet. In the spanwise direction, the velocity distribution is of approximately parabolic profile. METHODS (2) Experimental results indicate that porous woven meshes with Theoretical basis smaller pores produce less uniform injection velocities along The primary parameters that govern LAD performance are the the channel flow direction. The maximum injection velocity bubble point pressure and the total pressure loss. The bubble point non-uniformity may reach 30% for a 165 × 1500 DT mesh. In 29,30 pressure can be expressed using the Young–Laplace equation, thespanwisedirection,the velocity is not sensitive to the variation of the mesh specification. For the flow rate range ΔP ¼ 4γcosθ =D ; (11) BP c p considered in this study, the variation of flow rate has a where γ is the surface tension of the fluid; θ is the contact angle; negligible influence on velocity non-uniformity in both and D is the effective pore diameter of the porous woven mesh. directions. The total pressure loss inside the LAD channel should be less (3) A 3D model was proposed to predict the critical flow rate of than ΔP to prevent vapor penetration into the channel. For the BP the screen channel LAD, which considers the injection velocity experiments of Fig. 1a, The total pressure loss (ΔP ) is total non-uniformity in both streamwise and spanwise directions. expressed as The results of the 3D model were compared to experimental data to reveal an error of less than 8.4%, which indicates that ΔP ¼ ΔP þ ΔP þ ΔP þ ΔP þ ΔP ; total hydrostatic FTS friction dynamic other the model is reasonable. In particular, the accuracy of the 3D (12) modelismuchbetterthanthatofthe 1D and2Dmodels. (4) Microgravity influences the location of the vapor-liquid where ΔP is the hydrostatic pressure in the LAD channel, hydrostatic interface due to the dominance of the capillary force. Thus, ΔP is the FTS pressure drop, ΔP is the frictional loss inside FTS friction the middle of the LAD channel may be more likely to be the LAD channel, ΔP is the dynamic pressure drop, and dynamic exposed to vapor in microgravity conditions. However, ΔP is the pressure loss caused by vibration and fluid sloshing. other simulation results indicate that gravity has little influence on In microgravity environments, ΔP dominates the pressure loss FTS the velocity distribution for the wetted region and inside the term and influences the operational efficiency directly since the channel for single-phase flow. hydrostatic pressure is negligible . Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28 Z. Wang et al. According to Wang et al. , the FTS pressure drop can be pore geometries. The relevant parameters and the geometric expressed as properties of the test meshes are listed in Table 1. The PIV system (LaVision Inc.) included a high-speed camera ΔP ¼ A μv þ B ρv ; (13) FTS p p (4008 × 2672 pixels) and a laser pulse generator (Nd:YAG LASER NANO TRL, 425 mJ at 532 nm and 10 Hz). Particle motion was where A and B are FTS coefficients, which are determined by the p p captured by operating the high-speed camera at 2 Hz. The test geometry of the porous woven mesh; μ is the fluid viscosity; and ρ tank and the areas recorded using the PIV technique were shown is the fluid density. in Fig. 1c. The recorded area at yz plane starts at x = 105 mm, The maximum allowable liquid flow flux is referred to as the y = 5 mm, and z = 60 mm. With a 90% fill level, the vapor-liquid critical flow rate (Q ) and occurs when the total pressure loss is equal cr interface and channel bottom were located at z = 180 mm and to the bubble point pressure (ΔP ¼ ΔP ). Since the traditional total BP z = 0 mm, respectively. The laser was mounted perpendicular to 1D model assumes that the velocity across the porous woven mesh 10,23,25,31 the porous woven mesh at x = 105 mm, and thus the camera is uniform , the critical flow rate of the LAD could be captured particle motion across the yz plane of the porous mesh. calculated usind Eq. (6). However, recent studies have indicated a Due to the limited field-of-view, the size of the area recorded by large disparity between the critical flow rate derived from the 1D and the camera was limited to 80 × 165 mm. To test the spanwise experimental data, since the distribution of the fluid injection velocity distribution, three xy planes at z = 40 mm, 100 mm and velocity at the porous mesh plays an important role in the critical 160 mm were recorded. The orientations and positions of the flow rate, but was less considered in the previous studies . high-speed camera and the laser pulse generator were adjusted accordingly. Deionized water was chosen as the test fluid Experimental setup −3 −1 (ρ = 998.2 kg m , μ = 1.002 mPa s, and γ = 72.8 mN m ). Prior All the outflow tests of screen channel LAD were conducted in a to the experiments, water was doped with particles with transparent test tank made from quartz glass, a material that −3 diameters of 9 μm and density of 1.1 g cm , so that the particles’ exhibits good chemical stability and excellent optical properties volume fraction is around 0.002%. At such low concentrations, the (Supplementary Fig. 1). The size of the tank was 200 × 200 × tracking particles have been verified to have no obvious effect on 210 mm . The upper side of the test tank was a stainless-steel the water properties, including density, surface tension and plate affixed to the LAD channel with epoxy resin. It could also be 34,35 viscosity (<5%) . Experiments were conducted to recheck the removed from the test tank so that the LAD channel could be difference in bubble point pressures and contact angles between replaced and tests run under different conditions. The test system deionized water and doped water. The difference in bubble point −2 was placed at ground level with g = −9.8 m s . pressures was found to be within the experimental uncertainty. The LAD channel was a hollow duct composed of three The contact angle of deionized water and doped water show the transparent walls and a porous wall made from porous metal same value of 71 (±2)° on the stainless-steel plate (Supplementary mesh. The LAD channel was 15 mm long (L), 15 mm wide (W), and Fig. 3). Preliminary analysis also indicated that the particles would 200 mm high (H). The porous wall of the LAD channel was 85 mm not obviously clog the porous woven mesh during the tests away from the inner wall of the tank. Preliminary experiments (Supplementary Fig. 4) . A peristaltic pump was used to drain indicated that the distance had a negligible effect on the critical water from the channel and pumping it back into the test tank to flow rate provided that the distance was larger than 10 mm, as the maintain the fill level. The flow rate of the peristaltic pump could pressure loss caused by the distance between the porous wall and also be adjusted to achieve different working conditions. the inner wall is much smaller than the other items in Eq. (12). The bottom of the LAD channel is about 5 mm away from the wall of Data acquisition and reduction the tank. Considering the injection velocity is parallel to the Experiments were conducted at different flow rates for each type bottom wall, and the velocity magnitude is very low at the dead- of woven porous mesh. All of the test cases were repeated four end region, the distance is assumed to have no significant effect times to verify the consistency and repeatability, with each test on the LAD performance . Assembly of the LAD channel conducted at the steady state. The images captured using the proceeded as follows. Prior to the test, the porous woven mesh camera were analyzed via a cross-correlation algorithm using the was cleaned in an ultrasonic cleaner using alcohol and deionized LaVision PIV module and post-processed in MATLAB. The pressure water. The porous woven mesh was affixed to the channel using drop was detected using a pressure difference sensor with a range epoxy resin to avoid sealing and delamination at the edges. Two of 0–20 kPa. The flow rate was detected using two flow meters differential pressure transducers were mounted 25 mm apart at −1 −1 the bottom and top of the channel, as shown in Fig. 1c. with ranges of 4–40 L h and 40–400 L h , respectively. The Dutch Twill screens were used in the experiments since this uncertainty of the pressure difference sensor is 0.075%, while the type of mesh offers the smallest pore diameter and the most uncertainty of the flow rate is 1.5%. The diameter of particles is tortuous flow path. These features can prevent vapor ingestion . 1.7–1.9 pixels in the tracking images, and the measurement Three porous woven meshes with different pore sizes were uncertainty is between 0.05 and 0.1 px . Therefore, the uncer- chosen as experimental materials: an 80 × 700 Dutch Twill (DT) tainty of the PIV-derived velocity vectors is below 5.9%. mesh, a 130 × 1100 DT mesh, and a 165 × 1500 DT mesh. The porous meshes are labeled in the form n ´ n , where n and n w s w s Reporting summary denote the number of warp and shute wires per inch, respectively. Further information on research design is available in the Nature Prior to the experiments, the bubble point pressures of the Research Reporting Summary linked to this article. meshes were tested , and the effective pore diameter D was obtained based on Eq. (11) (Supplementary Methods, Supple- mentary Tables 2–4). The effective pore diameters overlap with DATA AVAILABILITY historical values considering the uncertainties caused by All data generated or analyzed during this study are included in this published article measurement and manufacturing. The diameters of wrap and and its supplementary information files. shute wires were obtained from scanning electron microscopy (SEM, by TESCAN VEGA3) images as shown in Supplementary Fig. 2, while the porosity ε, specific surface area S , hydraulic pore CODE AVAILABILITY diameter D (=4ε/S ), and the FTS pressure coefficients in Eq. (13) The code used to generate the plots are available from the corresponding author on h v were calculated according to the method of Wang et al. from the reasonable request. npj Microgravity (2022) 28 Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA Z. Wang et al. Received: 6 January 2022; Accepted: 13 July 2022; 29. Hartwig, J. & Mann, J. A. A predictive bubble point pressure model for porous liquid acquisition device screens. J. Porous Media 17, 587–600 (2014). 30. Hartwig, J., McQuillen, J. & Jurns, J. Screen channel liquid-acquisition-device bubble point tests in liquid oxygen. J. Thermophys. 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CFD simulation of Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims pressure drops in liquid acquisition device channel with sub-cooled oxygen. in published maps and institutional affiliations. World Acad. Sci., Eng. Technol. 58, 1180–1185 (2009). 23. Hartwig, J. W., Darr, S. R., McQuillen, J. B., Rame, E. & Chato, D. J. A steady state pressure drop model for screen channel liquid acquisition devices. Cryogenics 64, 260–271 (2014). Open Access This article is licensed under a Creative Commons 24. Wang, Y. et al. Analytical model of flow-through-screen pressure drop for metal Attribution 4.0 International License, which permits use, sharing, wire screens considering the effects of pore structures. Chem. Eng. Sci. 229, adaptation, distribution and reproduction in any medium or format, as long as you give 116037 (2021). appropriate credit to the original author(s) and the source, provide a link to the Creative 25. Hartwig, J. & Darr, S. Analytical model for steady flow through a finite channel Commons license, and indicate if changes were made. The images or other third party with one porous wall with arbitrary variable suction or injection. Phys. Fluids 26, material in this article are included in the article’s Creative Commons license, unless 123603 (2014). indicated otherwise in a credit line to the material. If material is not included in the 26. Darr, S. R., Camarotti, C. F., Hartwig, J. W. & Chung, J. N. Hydrodynamic model of article’s Creative Commons license and your intended use is not permitted by statutory screen channel liquid acquisition devices for in-space cryogenic propellant regulation or exceeds the permitted use, you will need to obtain permission directly management. Phys. Fluids 29, 017101 (2017). from the copyright holder. To view a copy of this license, visit http:// 27. Terzis, A. et al. Microscopic velocity field measurements inside a regular porous creativecommons.org/licenses/by/4.0/. medium adjacent to a low Reynolds number channel flow. Phys. Fluids 31, 042001 (2019). 28. Yang, G. et al. Pore-scale numerical simulations of flow and convective heat © The Author(s) 2022 transfer in a porous woven metal mesh. Chem. Eng. Sci. 256, 117696 (2022). Published in cooperation with the Biodesign Institute at Arizona State University, with the support of NASA npj Microgravity (2022) 28

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